DP Mathematical Studies Questionbank

• Syllabus

Topic 4 - Statistical applications

Sub sections and their related questions

4.1

• SPM.2.sl.TZ0.3a: Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show...
• SPM.2.sl.TZ0.3b: An egg is chosen at random. Find the probability that the egg is(i)     medium;(ii)    extra large.
• SPM.2.sl.TZ0.3c: There is a probability of \(0.3\) that a randomly chosen egg weighs more than \(w\) grams. Find...
• SPM.2.sl.TZ0.3d: The probability that a Brahma chicken produces a large size egg is \(0.121\). Frank’s Brahma...
• SPM.2.sl.TZ0.3e: The selling price, in US dollars (USD), of each size is shown in the table below.The probability...
• 14M.1.sl.TZ2.14a: Write down the probability that a randomly chosen tree has a height greater...
• 14M.1.sl.TZ2.14b: Write down the probability that a randomly chosen tree will be within 2 standard deviations of...
• 14M.1.sl.TZ2.14c: Use your graphic display calculator to calculate the probability that a randomly chosen tree will...
• 14M.1.sl.TZ2.14d: The probability that a particular tree is less than \(x\) metres high is \(0.65\). Find the value...
• 14M.2.sl.TZ1.5a: Draw a diagram that shows this information.
• 14M.2.sl.TZ1.5b: Write down the probability that a randomly chosen candidate who sat the Chemistry examination...
• 14M.2.sl.TZ1.5c: Hee Jin scored 80 marks in the Chemistry examination. Find the probability that a randomly...
• 14M.2.sl.TZ1.5d: The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\)...
• 14M.2.sl.TZ1.5e: The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\)...
• 14M.2.sl.TZ1.5f: To obtain a “grade A” a candidate must be in the top \(10\% \) of the candidates who sat the...
• 14N.1.sl.TZ0.12a: Calculate the probability that the temperature on a randomly chosen day in January is less than...
• 14N.1.sl.TZ0.12b: Calculate the expected number of days in January that the temperature will be more than 39°C.
• 14N.1.sl.TZ0.12c: On a randomly chosen day in January, the probability that the temperature is above \(T\) °C is...
• 15M.1.sl.TZ1.13a: Find the probability that a bag of rice chosen at random weighs between 990 g and 1004 g.
• 15M.1.sl.TZ1.13b: 95% of the bags of rice weigh less than \(k\) grams. Find the value of \(k\).
• 15M.1.sl.TZ1.13c: For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\). Find...
• 15M.1.sl.TZ2.13a: On the following diagram, shade the region representing the probability that a metal bar, chosen...
• 15M.1.sl.TZ2.13b: A metal bar is chosen at random. (i)     The probability that the length of the metal bar is...
• 15M.2.sl.TZ2.4b: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4c: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4d: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4e: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 16M.1.sl.TZ1.8a: The lifetime, \(L\) , of light bulbs made by a company follows a normal distribution.\(L\) is...
• 16M.1.sl.TZ1.8b: The standard deviation of the lifetime of the light bulbs is \(850\) hours. Find the probability...
• 16M.1.sl.TZ1.8c: The company states that \(90\% \) of the light bulbs have a lifetime of at least...
• 16N.2.sl.TZ0.4a: Draw a diagram that shows this information.
• 16N.2.sl.TZ0.4b: (i)     Find the probability that a box of cereal, chosen at random, is sold. (ii)     Calculate...
• 16N.2.sl.TZ0.4c: Calculate the manufacturer’s expected daily recycling cost.
• 16N.2.sl.TZ0.4d: Calculate the value of \(w\).
• 16M.2.sl.TZ2.3a: A speed camera on Peterson Road records the speed of each passing vehicle. The speeds are found...
• 16M.2.sl.TZ2.3b: A vehicle on Peterson Road is chosen at random. Find the probability that the speed of this...
• 16M.2.sl.TZ2.3c: It is found that \(19\,\% \) of the vehicles are exceeding the speed limit of...
• 16M.2.sl.TZ2.3d: There is a fine of \({\text{US}}\$ 65\) for exceeding the speed limit on Peterson Road. On a...
• 17M.1.sl.TZ2.11a: Write down the probability that the mass of one of these corncobs is greater than 400 grams.
• 17M.1.sl.TZ2.11b: Find the value of \(a\).
• 17M.1.sl.TZ2.11c: Estimate the interquartile range of the distribution.
• 17M.2.sl.TZ1.5a.i: Calculate the mean test grade of the students;
• 17M.2.sl.TZ1.5b: Find the median test grade of the students.
• 17M.2.sl.TZ1.5c: Find the interquartile range.
• 17M.2.sl.TZ1.5d: Find the probability that this student scored a grade 5 or higher.
• 17M.2.sl.TZ1.5e: Given that the first student chosen at random scored a grade 5 or higher, find the probability...
• 17M.2.sl.TZ1.5f.i: Calculate the probability that a student chosen at random spent at least 90 minutes preparing for...
• 17M.2.sl.TZ1.5f.ii: Calculate the expected number of students that spent at least 90 minutes preparing for the test.
• 17M.2.sl.TZ1.5a.ii: Calculate the standard deviation.
• 17N.1.sl.TZ0.13a: Find the probability that this applicant took at least 40 minutes to complete the test.
• 17N.1.sl.TZ0.13b: Find the value of \(k\).
• 17N.1.sl.TZ0.13c: Estimate the number of applicants who completed the test in less than 25 minutes.
• 18M.1.sl.TZ1.13a.i: Find the probability that a student, chosen at random arrives at least 60 minutes after the...
• 18M.1.sl.TZ1.13a.ii: Find the probability that a student, chosen at random arrives between 45 minutes and 55 minutes...
• 18M.1.sl.TZ1.13b: A second school, Mulberry Park, also opens at 08:00 every morning. The arrival times of the...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

4.2

• 10M.2.sl.TZ1.1a: Draw a scatter diagram to show the data. Use a scale of 2 cm to represent 10 metres on the x-axis...
• 10M.2.sl.TZ1.1b: Using your scatter diagram, describe the correlation between the number of different plant...
• 10M.2.sl.TZ1.1d: Plot the point (\(\bar x\), \(\bar y\)) on your scatter diagram. Label this point M.
• 11N.1.sl.TZ0.4a: Write down the correlation coefficient, \(r\) , for the examination scores.
• 12N.2.sl.TZ0.1b: Write down the correlation coefficient, r.
• 10M.2.sl.TZ2.2a: Draw a scatter diagram of the data. Use 1 cm to represent 1 hour and 1 cm to represent 10 km.
• 10M.2.sl.TZ2.2c: Mark and label the point \(M(\bar t,{\text{ }}\bar d)\) on your scatter diagram.
• 10M.2.sl.TZ2.2d: Draw the line of best fit on your scatter diagram.
• 12M.1.sl.TZ2.3a: Write down the value of (i) a ; (ii) b .
• 12M.1.sl.TZ2.3b: The mean of the x values is 5 and the mean of the y values is 4. Draw the line of best fit on the...
• 12M.1.sl.TZ2.3c: Use your line of best fit to estimate the value of y when x = 6.5.
• 09N.2.sl.TZ0.4A, b: The covariance, Sxy = 188.5. Write down the product-moment correlation coefficient, r.
• 11M.2.sl.TZ1.1d: Write down the product-moment correlation coefficient, \(r\) .
• 11M.2.sl.TZ1.1c: Plot the point \((\bar x{\text{, }}\bar y)\) on your scatter diagram and label this point M .
• 11M.2.sl.TZ1.1a: Draw a scatter diagram to show the above data. Use a scale of \(2{\text{ cm}}\) to represent...
• 13M.2.sl.TZ2.2a: Draw a scatter diagram to show the relationship between the mass of a chicken and its cooking...
• 07M.2.sl.TZ0.1e: A sample of 15 of the fish was weighed. The weight, W was plotted against length, L as shown...
• 11M.2.sl.TZ2.1B.a: Draw a labelled scatter diagram for this data. Use a scale of \(2{\text{ cm}}\) to represent...
• 13M.2.sl.TZ1.3g: George decides to model the change in temperature of the coffee with a linear function using...
• 11M.2.sl.TZ2.1B.c: Plot the point \({\text{M}}(\bar S{\text{, }}\bar F)\) on your scatter diagram.
• 13M.2.sl.TZ2.2d: Draw the line of best fit on the scatter diagram.
• 13M.2.sl.TZ2.2e: Using your line of best fit, estimate the cooking time, in minutes, for a 1.7 kg chicken.
• 13M.2.sl.TZ2.2f: Write down the Pearson’s product–moment correlation coefficient, r .
• 13M.2.sl.TZ2.2g: Using your value for r , comment on the correlation.
• 13M.2.sl.TZ2.2h: The cooking time of an additional 2.0 kg chicken is recorded. If the mass and cooking time of...
• SPM.1.sl.TZ0.4b: Write down the value of \(r\), the Pearson’s product-moment correlation coefficient for this set...
• 07N.1.sl.TZ0.14c: Use your graphic display calculator to find the correlation coefficient r.
• 07N.1.sl.TZ0.14d: Comment on your value for r.
• 08N.1.sl.TZ0.11a: Write down the product moment correlation coefficient, \(r\).
• 08M.2.sl.TZ1.3b: Write down the correlation coefficient, \(r\), for the variables \(n\) and \(T\).
• 08M.2.sl.TZ1.3c: Comment on your value for \(r\).
• 08M.2.sl.TZ2.2ii.a: Plot these pairs of values on a scatter diagram. Use a scale of \(1{\text{ cm}}\) to represent...
• 08M.2.sl.TZ2.2ii.b: Write down the linear correlation coefficient, \(r\), for the data.
• 14M.1.sl.TZ2.12b: Write down the value of the Pearson’s product–moment correlation coefficient, \(r\).
• 13N.2.sl.TZ0.1a: Draw a scatter diagram for the above data. Use a scale of \(1\) cm to represent \(10\) km on the...
• 13N.2.sl.TZ0.1c: Plot and label the point \({\text{M }}(\bar x,{\text{ }}\bar y)\) on your scatter diagram.
• 13N.2.sl.TZ0.1d: Use your graphic display calculator to find (i)     the product–moment correlation coefficient,...
• 14M.2.sl.TZ1.1b: On graph paper, draw a scatter diagram to show Barry’s results. Use a scale of 1 cm to represent...
• 14M.2.sl.TZ1.1d: Plot and label the point \({\text{M}}(\bar x,{\text{ }}\bar y)\) on your graph.
• 14M.2.sl.TZ1.1e: Write down (i)     the Pearson’s product–moment correlation coefficient, \(r\), for Barry’s...
• 14N.2.sl.TZ0.1a: Draw the scatter diagram for the above data. Use a scale of 2 cm for 20 chirps on the horizontal...
• 14N.2.sl.TZ0.1b: Use your graphic display calculator to write down the Pearson’s product–moment correlation...
• 14N.2.sl.TZ0.1c: Interpret the relationship between \(x\) and \(T\) using your value of \(r\).
• 14N.2.sl.TZ0.1f: Given that \(\bar x = 70\), draw the regression line \(T\) on \(x\) on your scatter diagram.
• 15M.1.sl.TZ1.4a: Find (i)     Pearson’s product–moment correlation coefficient, \(r\); (ii)     the equation of...
• 15M.2.sl.TZ2.6a: (i)     Write down the Pearson’s product–moment correlation coefficient, \(r\), for these...
• 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
• 16M.2.sl.TZ1.1b: Calculate i)      \({\bar x}\) , the mean distance from the power plant; ii)     \({\bar y}\) ,...
• 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
• 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
• 16M.1.sl.TZ2.9a: Each day a supermarket records the midday temperature and how many cold drinks are sold on that...
• 16M.1.sl.TZ2.9b: Draw the line of best fit on the scatter diagram.
• 16M.1.sl.TZ2.9c: Use the line of best fit to estimate the number of cold drinks that are sold on a day when the...
• 16N.2.sl.TZ0.1a: On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours...
• 16N.2.sl.TZ0.1b: (i)     \({\bar x}\), the mean number of hours spent on social media; (ii)     \({\bar y}\), the...
• 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
• 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for these data.
• 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
• 17M.2.sl.TZ1.1a: Find the range of the average body weights for these seven species of mammal.
• 17M.2.sl.TZ1.1b.i: For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation...
• 17M.2.sl.TZ1.1b.ii: For the data from these seven species describe the correlation between the average body weight...
• 17M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).
• 17M.2.sl.TZ1.1d: Use your regression line to estimate the average weight of the brain of grey wolves.
• 17M.2.sl.TZ1.1e: Find the percentage error in your estimate in part (d).
• 17M.2.sl.TZ1.1f: State whether it is valid to use the regression line to estimate the average weight of the brain...
• 17M.2.sl.TZ2.3a: Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis...
• 17M.2.sl.TZ2.3b.i: Write down, for this set of data the mean number of folders produced, \(\bar x\);
• 17M.2.sl.TZ2.3b.ii: Write down, for this set of data the mean production cost, \(\bar C\).
• 17M.2.sl.TZ2.3c: Label the point \({\text{M}}(\bar x,{\text{ }}\bar C)\) on the scatter diagram.
• 17M.2.sl.TZ2.3d: Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient,...
• 17M.2.sl.TZ2.3e: State a reason why the regression line \(C\) on \(x\) is appropriate to model the relationship...
• 17M.2.sl.TZ2.3f: Use your graphic display calculator to find the equation of the regression line \(C\) on \(x\).
• 17M.2.sl.TZ2.3g: Draw the regression line \(C\) on \(x\) on the scatter diagram.
• 17M.2.sl.TZ2.3h: Use the equation of the regression line to estimate the least number of folders that the factory...
• 17N.1.sl.TZ0.5a: Find the mean number of hours that the people surveyed watch television per week.
• 17N.1.sl.TZ0.5b: Draw the regression line on the scatter diagram.
• 17N.1.sl.TZ0.5c: By placing a tick (✔) in the correct box, determine which of the following statements is true:
• 17N.1.sl.TZ0.5d: Diogo is 18 years old. Give a reason why the regression line should not be used to estimate the...
• 18M.1.sl.TZ1.4a.i: For these data, find Pearson’s product-moment correlation coefficient, r.
• 18M.1.sl.TZ1.4a.ii: For these data, find the equation of the regression line y on x.
• 18M.1.sl.TZ1.4b: Using the equation of the regression line, estimate the concentration of dissolved oxygen in the...
• 18M.1.sl.TZ2.1a: Plot and label the point M\(\left( {\bar m,\,\,\bar p} \right)\) on the scatter diagram.
• 18M.1.sl.TZ2.1b: Draw the line of best fit, by eye, on the scatter diagram.
• 18M.1.sl.TZ2.1c: Using your line of best fit, estimate the physics test score for a student with a score of 20 in...

4.3

• 10M.2.sl.TZ1.1e: Write down the equation of the regression line y on x for the above data.
• 10M.2.sl.TZ1.1f: Draw the regression line y on x on your scatter diagram.
• 10M.2.sl.TZ1.1g: Estimate the number of plant species growing 30 metres from the lake shore.
• 11N.1.sl.TZ0.4b: Write down the equation of the regression line, \(y\) on \(x\) , for the examination scores of...
• 11N.1.sl.TZ0.4c: A sixth candidate scored 72 in the Mathematics examination. Use the regression line, \(y\) on...
• 12N.2.sl.TZ0.1c: Write down the equation of the regression line of y on x.
• 12N.2.sl.TZ0.1d: Another golfer scored 70 in Round 1. Calculate an estimate of his score in Round 2.
• 12N.2.sl.TZ0.1e: Another golfer scored 89 in Round 1. Determine whether you can use the equation of the...
• 12M.1.sl.TZ1.11a: Use your graphic display calculator to write down the equation of the regression line for y on x...
• 12M.1.sl.TZ1.11b: Use your equation to estimate the number of calories that a person will burn during a 17 minute...
• 12M.1.sl.TZ1.11c: State whether your answer to part (b) is reliable. Give a reason for your answer.
• 10M.2.sl.TZ2.2e: Using your graph, estimate the time when Alex and Kris pass the 85 km distance marker. Give your...
• 10M.2.sl.TZ2.2f: Write down the equation of the regression line for the data given.
• 10M.2.sl.TZ2.2g.i: Using your equation calculate the distance marker passed by the cyclists at 10.3 hours.
• 12M.1.sl.TZ2.3c: Use your line of best fit to estimate the value of y when x = 6.5.
• 09N.2.sl.TZ0.4A, c: Write down the equation of the regression line of y on x.
• 09N.2.sl.TZ0.4A, d: If the number of trees in an area is 55, estimate the depth of snow.
• 09N.2.sl.TZ0.4A, e, i: Use the equation of the regression line to estimate the depth of snow in an area with 100 trees.
• 11M.2.sl.TZ1.1g: The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . State, with a...
• 11M.2.sl.TZ1.1f: The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Estimate the heat...
• 11M.2.sl.TZ1.1e: The equation of the regression line \(y\) on \(x\) is \(y = - 0.470x + 83.7\) . Draw the...
• 07M.2.sl.TZ0.1e: A sample of 15 of the fish was weighed. The weight, W was plotted against length, L as shown...
• 09M.1.sl.TZ2.6a: Write down the equation of the regression line for s on t.
• 09M.1.sl.TZ2.6b: Use your equation to predict the ice cream sales on a day when the maximum temperature is 24 °C....
• 13M.2.sl.TZ1.3g: George decides to model the change in temperature of the coffee with a linear function using...
• 13M.2.sl.TZ1.3h: Use the equation of the regression line to estimate the temperature of the coffee at t = 3.
• 11M.2.sl.TZ2.1B.d: Use your graphic display calculator to find the equation of the regression line of \(F\) on \(S\)...
• 11M.2.sl.TZ2.1B.e: Draw the regression line on your scatter diagram.
• 11M.2.sl.TZ2.1B.f: Carletta’s mark on the Science examination was \(44\). She did not sit the French examination....
• 11M.2.sl.TZ2.1B.g: Monique’s mark on the Science examination was 85. She did not sit the French examination. Her...
• SPM.1.sl.TZ0.4c: Draw the regression line for \(y\) on \(x\) on the set of axes above.
• 07N.1.sl.TZ0.14a: Use your graphic display calculator to find the equation of the regression line of y on x.
• 07N.1.sl.TZ0.14b: Use your equation to estimate the number of objects remembered by a person aged 28 years.
• 08N.1.sl.TZ0.11b: Write down, in the form \(y = mx + c\) , the equation of the regression line \(y\) on \(x\) for...
• 08N.1.sl.TZ0.11c: A ninth candidate obtained a score of \(7\) in the Physics test but was absent for the Chemistry...
• 08N.1.sl.TZ0.11d: Give a reason why it is valid to use this regression line to estimate the score on the Chemistry...
• 08M.2.sl.TZ1.3d: The equation of the line of regression for \(n\) on \(T\) is \(n = dT - 100\). (i)     Write...
• 08M.2.sl.TZ1.3e: On a day when the temperature was \({36^ \circ }\) Peter calculates that \(314\) bottles would be...
• 08M.2.sl.TZ2.2ii.c: Stephen wishes to buy a paperback book which has \(350\) pages in it. He plans to draw a line of...
• 09N.2.sl.TZ0.4A, e, ii: Decide whether the answer in (e)(i) is a valid estimate of the depth of snow in the area. Give a...
• 10M.2.sl.TZ2.2g.ii: Is this estimate of the distance reliable? Give a reason for your answer.
• 14M.1.sl.TZ2.12a: Use your graphic display calculator to write down the equation of the regression line \(t\) on...
• 14M.1.sl.TZ2.12c: Use your regression equation to find the amount of time 4 cleaners take to clean the school.
• 13N.2.sl.TZ0.1d: Use your graphic display calculator to find (i)     the product–moment correlation coefficient,...
• 13N.2.sl.TZ0.1e: Draw the regression line \(y\) on \(x\) on your scatter diagram.
• 13N.2.sl.TZ0.1f: A ninth regional station is \(76\) km from the city centre terminus. Use the equation of the...
• 13N.2.sl.TZ0.1g: Give a reason why it is valid to use your regression line to estimate the price of this return...
• 14M.2.sl.TZ1.1e: Write down (i)     the Pearson’s product–moment correlation coefficient, \(r\), for Barry’s...
• 14M.2.sl.TZ1.1f: Draw the regression line \(y\) on \(x\) on your graph.
• 14M.2.sl.TZ1.1g: Use the equation of the regression line \(y\) on \(x\) to estimate the circumference of a tree...
• 14N.2.sl.TZ0.1d: Use your graphic display calculator to write down the equation of the regression line \(T\) on...
• 14N.2.sl.TZ0.1e: Calculate the air temperature when the cricket’s chirp rate is \(70\).
• 14N.2.sl.TZ0.1f: Given that \(\bar x = 70\), draw the regression line \(T\) on \(x\) on your scatter diagram.
• 14N.2.sl.TZ0.1h: A cricket makes 20 chirps in 15 seconds. For this chirp rate (i)     calculate an estimate for...
• 15M.1.sl.TZ1.4a: Find (i)     Pearson’s product–moment correlation coefficient, \(r\); (ii)     the equation of...
• 15M.1.sl.TZ1.4b: Use the equation of the regression line \(y\) on \(x\) to estimate the number of mosquitoes...
• 15M.2.sl.TZ2.6b: Write down the equation of the regression line \(y\) on \(x\) for these data, in the form...
• 15M.2.sl.TZ2.6c: Estimate the total cost, to the nearest USD, of producing \(13\) bicycles on a particular day.
• 15M.2.sl.TZ2.6d: All the bicycles that are produced are sold. The bicycles are sold for 304 USD each. Explain why...
• 15M.2.sl.TZ2.6e: All the bicycles that are produced are sold. The bicycles are sold for 304 USD each. (i)    ...
• 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
• 16M.2.sl.TZ1.1b: Calculate i)      \({\bar x}\) , the mean distance from the power plant; ii)     \({\bar y}\) ,...
• 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
• 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
• 16N.2.sl.TZ0.1a: On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours...
• 16N.2.sl.TZ0.1b: (i)     \({\bar x}\), the mean number of hours spent on social media; (ii)     \({\bar y}\), the...
• 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
• 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for these data.
• 16N.2.sl.TZ0.1e: Write down the equation of the regression line \(y\) on \(x\) for these eight male students.
• 16N.2.sl.TZ0.1f: Draw the regression line, from part (e), on your scatter diagram.
• 16N.2.sl.TZ0.1g: Use the given equation of the regression line to estimate the number of IB Diploma points that...
• 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
• 17M.2.sl.TZ1.1a: Find the range of the average body weights for these seven species of mammal.
• 17M.2.sl.TZ1.1b.i: For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation...
• 17M.2.sl.TZ1.1b.ii: For the data from these seven species describe the correlation between the average body weight...
• 17M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).
• 17M.2.sl.TZ1.1d: Use your regression line to estimate the average weight of the brain of grey wolves.
• 17M.2.sl.TZ1.1e: Find the percentage error in your estimate in part (d).
• 17M.2.sl.TZ1.1f: State whether it is valid to use the regression line to estimate the average weight of the brain...
• 17M.2.sl.TZ2.3a: Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis...
• 17M.2.sl.TZ2.3b.i: Write down, for this set of data the mean number of folders produced, \(\bar x\);
• 17M.2.sl.TZ2.3b.ii: Write down, for this set of data the mean production cost, \(\bar C\).
• 17M.2.sl.TZ2.3c: Label the point \({\text{M}}(\bar x,{\text{ }}\bar C)\) on the scatter diagram.
• 17M.2.sl.TZ2.3d: Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient,...
• 17M.2.sl.TZ2.3e: State a reason why the regression line \(C\) on \(x\) is appropriate to model the relationship...
• 17M.2.sl.TZ2.3f: Use your graphic display calculator to find the equation of the regression line \(C\) on \(x\).
• 17M.2.sl.TZ2.3g: Draw the regression line \(C\) on \(x\) on the scatter diagram.
• 17M.2.sl.TZ2.3h: Use the equation of the regression line to estimate the least number of folders that the factory...
• 17N.1.sl.TZ0.5a: Find the mean number of hours that the people surveyed watch television per week.
• 17N.1.sl.TZ0.5b: Draw the regression line on the scatter diagram.
• 17N.1.sl.TZ0.5c: By placing a tick (✔) in the correct box, determine which of the following statements is true:
• 17N.1.sl.TZ0.5d: Diogo is 18 years old. Give a reason why the regression line should not be used to estimate the...
• 18M.1.sl.TZ1.4a.i: For these data, find Pearson’s product-moment correlation coefficient, r.
• 18M.1.sl.TZ1.4a.ii: For these data, find the equation of the regression line y on x.
• 18M.1.sl.TZ1.4b: Using the equation of the regression line, estimate the concentration of dissolved oxygen in the...

4.4

• 10M.1.sl.TZ1.10a: State the null hypothesis, H0, for this test.
• 10M.1.sl.TZ1.10b: Write down the number of degrees of freedom.
• 10M.1.sl.TZ1.10c: Of the 400 people Tony interviewed, 220 were male and 180 were female. 80 of the people had...
• 10M.1.sl.TZ1.10d: Tony used a 5 % level of significance for his test and obtained a p-value of 0.0634 correct to 3...
• 10M.1.sl.TZ2.9a.i: Write down the null hypothesis.
• 10M.1.sl.TZ2.9b: Write down the number of degrees of freedom for this test.
• 10M.1.sl.TZ2.9c: Write down the critical value for this test.
• 10M.1.sl.TZ2.9d: State whether the type of coffee drunk is independent of gender. Give a reason for your answer.
• 10N.2.sl.TZ0.1B.a: Write down the null hypothesis, H0, for this test.
• 10N.2.sl.TZ0.1B.b: Write down the number of degrees of freedom for this test.
• 10N.2.sl.TZ0.1B.d: Show that the expected number of females that have more than 5 meals per day is 13, correct to...
• 10N.2.sl.TZ0.1B.e: Use your graphic display calculator to find the \(\chi _{calc}^2\) for this data.
• 10N.2.sl.TZ0.1B.f: Decide whether H0 must be accepted. Justify your answer.
• 10N.2.sl.TZ0.1B.c: Write down the critical value for this test.
• 12N.2.sl.TZ0.4b: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12N.2.sl.TZ0.4c: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12N.2.sl.TZ0.4d: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12N.2.sl.TZ0.4e: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12N.2.sl.TZ0.4f: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12N.2.sl.TZ0.4g: The manager of the store wants to determine whether the screen size is independent of gender. A...
• 12M.2.sl.TZ1.2a: Write down the null hypothesis, H0, for this test.
• 12M.2.sl.TZ1.2b: Find the expected value of female footballers.
• 12M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
• 12M.2.sl.TZ1.2d: Write down the critical value of \(\chi ^2\), at the 5 % level of significance.
• 12M.2.sl.TZ1.2e: Use your graphic display calculator to determine the \(\chi _{calc}^2\) value.
• 12M.2.sl.TZ1.2f: Determine whether H0 should be accepted. Justify your answer.
• 12M.1.sl.TZ2.8a: Write down the null hypothesis.
• 12M.1.sl.TZ2.8b: The colours of the cars were red, green, blue, black and silver. Find the number of degrees of...
• 12M.1.sl.TZ2.8c: At the 5 % significance level the \(\chi_{calc}^2\) was found to be 8.73. Write down the...
• 11N.2.sl.TZ0.2c: Pam decides to test her belief using a Chi-squared test at the \(5\% \) level of...
• 11N.2.sl.TZ0.2d: Write down (i)     the Chi-squared calculated value; (ii)    the number of degrees of...
• 11N.2.sl.TZ0.2e: State, giving a reason, whether there is sufficient evidence at the \(5\% \) level of...
• 09N.2.sl.TZ0.4B, a: Write down the total number of male students.
• 09N.2.sl.TZ0.4B, b: Show that the expected frequency for males, whose favourite car colour is blue, is 12.6.
• 09N.2.sl.TZ0.4B, c, i: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
• 09M.1.sl.TZ1.6a: Find the number of degrees of freedom for the \(\chi^2\) test.
• 09M.1.sl.TZ1.6b: Write down the null hypothesis for the \(\chi^2\) test.
• 09M.1.sl.TZ1.6d: The critical value for the \(\chi^2\) test at the 5% significance level is 12.59. The \(\chi^2\)...
• 07N.2.sl.TZ0.4ii.a: Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.
• 11M.2.sl.TZ1.2B.d: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
• 11M.2.sl.TZ1.2B.e: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
• 11M.2.sl.TZ1.2B.f: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
• 11M.2.sl.TZ1.2B.g: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
• 09M.2.sl.TZ2.2i, a: Write down the null and alternative hypotheses for this test.
• 09M.2.sl.TZ2.2i, b: For the number of fertilized plants with height greater than 75 cm, show that the expected value...
• 09M.2.sl.TZ2.2i, c: Write down the value of \(\chi_{calc}^2\).
• 09M.2.sl.TZ2.2i, d: Write down the number of degrees of freedom.
• 09M.2.sl.TZ2.2i, f: Is the manufacturer’s claim justified? Give a reason for your answer.
• 11M.2.sl.TZ2.1A.e: State whether Ludmila accepts the null hypothesis. Give a reason for your answer.
• 11M.2.sl.TZ2.1A.d: Use your graphic display calculator to find the \({\chi ^2}\) test statistic for this data.
• 11M.2.sl.TZ2.1A.c: Find the expected frequency for the females studying Spanish.
• 11M.2.sl.TZ2.1A.b: Write down the number of degrees of freedom.
• 11M.2.sl.TZ2.1A.a: State Ludmila’s null hypothesis.
• 13M.2.sl.TZ1.1a: State the null hypothesis, H0, for the test.
• 13M.2.sl.TZ1.1b: Write down the number of degrees of freedom.
• 13M.2.sl.TZ1.1c: Write down the critical value for the test.
• 13M.2.sl.TZ1.1d: Show that the expected number of Medium Yield crops using Fertilizer C is 17, correct to the...
• 13M.2.sl.TZ1.1e: Use your graphic display calculator to find for the data (i) the \(\chi^2\) calculated value,...
• 13M.2.sl.TZ1.1f: State the conclusion of the test. Give a reason for your decision.
• 13M.1.sl.TZ2.6a: Write down the null hypothesis.
• 13M.1.sl.TZ2.6b: Find the number of degrees of freedom for this test.
• 13M.1.sl.TZ2.6c: Write down the critical value for this test.
• 13M.1.sl.TZ2.6d: State the conclusion of this test. Give a reason for your decision.
• 07M.1.sl.TZ0.8a: Write a suitable null hypothesis for a \(\chi^2\) test on this data.
• 07M.1.sl.TZ0.8b: Write down the value of \(\chi^2\) for this data.
• 07M.1.sl.TZ0.8c: The number of degrees of freedom is 4. Show how this value is calculated.
• 07M.1.sl.TZ0.8d: The critical value, at the 5% level of significance, is 9.488. What conclusion can be drawn from...
• SPM.1.sl.TZ0.8a: Find the expected number of female volleyball players under this hypothesis.
• SPM.1.sl.TZ0.8b: Write down the \(p\)-value for the test.
• SPM.1.sl.TZ0.8c: State, with a reason, the conclusion of the test.
• 07N.2.sl.TZ0.4ii.b: State Manuel’s null hypothesis and alternative hypothesis.
• 07N.2.sl.TZ0.4ii.c: Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched...
• 07N.2.sl.TZ0.4ii.d: Using your graphic display calculator, or otherwise, find the chi-squared statistic for Manuel’s...
• 07N.2.sl.TZ0.4ii.e: (i) State the number of degrees of freedom available for this calculation. (ii) State his...
• 08N.2.sl.TZ0.3a: Jorge applies a \({\chi ^2}\) test at the \(5\% \) level to investigate whether wearing a seat...
• 08M.1.sl.TZ1.5a: Write down the null hypothesis.
• 08M.1.sl.TZ1.5b: Write down the number of degrees of freedom.
• 08M.1.sl.TZ1.5c: Write down the chi-squared value.
• 08M.1.sl.TZ1.5d: State whether or not you will reject the null hypothesis, giving a clear reason for your answer.
• 08M.2.sl.TZ2.2i.c: The market research organization tests the survey data to determine whether the brand of cereal...
• 08M.2.sl.TZ2.2i.d: The market research organization tests the survey data to determine whether the brand of cereal...
• 08M.2.sl.TZ2.2i.e: The market research organization tests the survey data to determine whether the brand of cereal...
• 08M.2.sl.TZ2.2i.f: The market research organization tests the survey data to determine whether the brand of cereal...
• 08M.2.sl.TZ2.2i.g: The market research organization tests the survey data to determine whether the brand of cereal...
• 09N.2.sl.TZ0.4B, c, ii: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
• 09N.2.sl.TZ0.4B, c, iv: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
• 10M.1.sl.TZ2.9a.ii: Write down the alternative hypothesis.
• 14M.1.sl.TZ2.8a: Find the expected frequency for the females who use public transport to get to school.
• 14M.1.sl.TZ2.8b: Find the \({\chi ^2}\) statistic.
• 14M.1.sl.TZ2.8c: The \({\chi ^2}\) critical value is \(7.815\) at the \(5\%\) significance level. State whether...
• 13N.1.sl.TZ0.8a: Write down the null hypothesis for this test.
• 13N.1.sl.TZ0.8b: Write down the number of degrees of freedom.
• 13N.1.sl.TZ0.8c: Write down the value of \(\chi _{calc}^2\).
• 13N.1.sl.TZ0.8d: The critical value, at the \(5\%\) significance level, is \(7.815\). State, giving a reason, the...
• 14M.1.sl.TZ1.4a: State the null hypothesis.
• 14M.1.sl.TZ1.4b: Write down the number of degrees of freedom.
• 14M.1.sl.TZ1.4c: Write down (i)     the \({\chi ^2}\) statistic; (ii)     the associated p-value.
• 14M.1.sl.TZ1.4d: State, giving a reason, whether the null hypothesis should be accepted.
• 14N.1.sl.TZ0.10a: State Minta’s null hypothesis.
• 14N.1.sl.TZ0.10b: State the number of degrees of freedom.
• 14N.1.sl.TZ0.10c: 150 students showed a preference for a smoothie. Calculate the expected number of female...
• 14N.1.sl.TZ0.10d: Minta found that the calculated value of the \({\chi ^2}\) test was 3.576. The critical value at...
• 15M.1.sl.TZ2.7a: Write down the null hypothesis for this test.
• 15M.1.sl.TZ2.7b: Write down the observed number of viewers who preferred Rumba and were older than 20 years old.
• 15M.1.sl.TZ2.7c: Use your graphic display calculator to find the \(p\)-value for this test.
• 15M.1.sl.TZ2.7d: The producer claims that the type of Latin dance a viewer preferred is independent of their...
• 15M.2.sl.TZ1.1a: State (i)     \({{\text{H}}_0}\), the null hypothesis for the test; (ii)    ...
• 15M.2.sl.TZ1.1b: Write down the number of degrees of freedom.
• 15M.2.sl.TZ1.1c: Show that the expected frequency of those between the ages of 26 and 40 who oppose the reduction...
• 15M.2.sl.TZ1.1d: Find (i)     the \({\chi ^2}\) statistic; (ii)     the associated \(p\)-value for the test.
• 15M.2.sl.TZ1.1e: Determine, giving a reason, whether \({{\text{H}}_0}\) should be accepted.
• 16M.1.sl.TZ1.10a: The manager of a travel agency surveyed 1200 travellers. She wanted to find out whether there was...
• 16M.1.sl.TZ1.10b: Find the number of degrees of freedom.
• 16M.1.sl.TZ1.10c: The critical value of this \(\chi {\,^2}\) test is \(21.026\). Use this information to write...
• 16M.1.sl.TZ1.10d: From the travellers taking part in the survey, 285 were 61 years or older and 420 preferred...
• 16N.1.sl.TZ0.6a: Find the expected frequency of the patients who became infected whilst in Nightingale ward.
• 16N.1.sl.TZ0.6b: For this test, write down the \({\chi ^2}\) statistic.
• 16N.1.sl.TZ0.6c: State, giving a reason, whether the null hypothesis should be rejected.
• 16M.1.sl.TZ2.7a: A survey was conducted among a random sample of people about their favourite TV show. People were...
• 16M.1.sl.TZ2.7b: A \({\chi ^{\,2}}\) test at the \(5\,\% \) significance level is used to determine whether TV...
• 16M.1.sl.TZ2.7c: State the conclusion of the test. Give a reason for your answer.
• 17M.1.sl.TZ1.6a: Write down the value of \(x\).
• 17M.1.sl.TZ1.6b: Write down the number of degrees of freedom for this test.
• 17M.1.sl.TZ1.6c: Use your graphic display calculator to find the \({\chi ^2}\) statistic for this test.
• 17M.1.sl.TZ1.6d: State the conclusion for this test. Give a reason for your answer.
• 17M.2.sl.TZ2.1a.i: If the teacher chooses a response at random, find the probability that it is a response to the...
• 17M.2.sl.TZ2.1a.ii: If the teacher chooses a response at random, find the probability that it is a satisfactory...
• 17M.2.sl.TZ2.1a.iii: If the teacher chooses a response at random, find the probability that it is a satisfactory...
• 17M.2.sl.TZ2.1b: The teacher groups the responses by topic, and chooses two responses to the Logic question. Find...
• 17M.2.sl.TZ2.1c: State the null hypothesis for this test.
• 17M.2.sl.TZ2.1d: Show that the expected frequency of satisfactory Calculus responses is 12.
• 17M.2.sl.TZ2.1e: Write down the number of degrees of freedom for this test.
• 17M.2.sl.TZ2.1f: Use your graphic display calculator to find the \({\chi ^2}\) statistic for this data.
• 17M.2.sl.TZ2.1g: State the conclusion of this \({\chi ^2}\) test. Give a reason for your answer.
• 17N.2.sl.TZ0.1a: State whether \(N\) is a discrete or a continuous variable.
• 17N.2.sl.TZ0.1b.i: Write down, for \(N\), the modal class;
• 17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
• 17N.2.sl.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
• 17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
• 17N.2.sl.TZ0.1d: Find the expected frequency of students choosing the Science category and obtaining 31 to 40...
• 17N.2.sl.TZ0.1e.i: Write down the null hypothesis for this test;
• 17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
• 17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
• 17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
• 17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
• 18M.2.sl.TZ1.2a: State the alternative hypothesis.
• 18M.2.sl.TZ1.2b: Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
• 18M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
• 18M.2.sl.TZ1.2d.i: Write down the χ2 statistic.
• 18M.2.sl.TZ1.2d.ii: Write down the associated p-value.
• 18M.2.sl.TZ1.2e: State, with a reason, whether you would reject the null hypothesis.
• 18M.2.sl.TZ1.2f: Write down the probability that this flight arrived on time.
• 18M.2.sl.TZ1.2h: Two flights are chosen at random from those which were slightly delayed. Find the probability...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.