DP Mathematics HL Questionbank

• Syllabus

7.6

Sub sections and their related questions

Null and alternative hypotheses, \({H_0}\) and \({H_1}\) .

• 12M.3sp.hl.TZ0.1b: In spite of these results the baker insists that his claim is correct. Stating appropriate...
• 12N.3sp.hl.TZ0.3a: The random variable X represents the height of a wave on a particular surf beach. It is known...
• 12N.3sp.hl.TZ0.3b: The random variable Y represents the height of a wave on another surf beach. It is known that Y...
• 11M.3sp.hl.TZ0.3b: (i)     State suitable hypotheses for testing whether or not this diet causes a mean loss in...
• 11M.3sp.hl.TZ0.4a: Calculate the significance level of the test.
• 11M.3sp.hl.TZ0.4b: Given that the value of \(\mu \) is actually 2.5, determine the probability of a Type II error.
• SPNone.3sp.hl.TZ0.1c: The stallholder claims that the mean weight of apples is 125 grams but the shopper claims that...
• 10M.3sp.hl.TZ0.2: The random variable X has a Poisson distribution with mean \(\mu \). The value of \(\mu \) is...
• 13M.3sp.hl.TZ0.1c: Given the hypotheses \[{{\text{H}}_0}:\mu  = 15;{\text{ }}{{\text{H}}_1}:\mu  \ne 15,\] find...
• 13M.3sp.hl.TZ0.3a: State suitable hypotheses for this investigation.
• 13M.3sp.hl.TZ0.3b: It is decided to define the critical region by \(x \leqslant 25\). (i)     Calculate the...
• 13N.3sp.hl.TZ0.3c: (i)     State the meaning of a type II error. (ii)     Write down how to proceed if it is...
• 13N.3sp.hl.TZ0.4: Francisco and his friends want to test whether performance in running 400 metres improves if they...
• 13N.3sp.hl.TZ0.3b: Explain what can be done with this data to decrease the probability of making a type I error.
• 15M.3sp.hl.TZ0.2b: (i)     State suitable hypotheses to test the claim that extra tuition improves examination...
• 18M.3sp.hl.TZ0.3a: State suitable hypotheses for a two-tailed test.
• 18M.3sp.hl.TZ0.3b: Find the critical region for testing \({\bar b}\) at the 5 % significance level.
• 18M.3sp.hl.TZ0.3c: Find the probability of making a Type II error.

Significance level.

• 12M.3sp.hl.TZ0.1b: In spite of these results the baker insists that his claim is correct. Stating appropriate...
• 18M.3sp.hl.TZ0.3a: State suitable hypotheses for a two-tailed test.
• 18M.3sp.hl.TZ0.3b: Find the critical region for testing \({\bar b}\) at the 5 % significance level.
• 18M.3sp.hl.TZ0.3c: Find the probability of making a Type II error.

Critical regions, critical values, \(p\)-values, one-tailed and two-tailed tests.

• 12M.3sp.hl.TZ0.1b: In spite of these results the baker insists that his claim is correct. Stating appropriate...
• 08M.3sp.hl.TZ1.1: A coin was tossed 200 times and 115 of these tosses resulted in ‘heads’. Use a two-tailed test...
• 08M.3sp.hl.TZ2.2: A factory makes wine glasses. The manager claims that on average 2 % of the glasses are...
• 08M.3sp.hl.TZ2.5: (a)     Find the appropriate critical regions corresponding to a significance level of   (i)    ...
• 09N.3sp.hl.TZ0.1: The mean weight of a certain breed of bird is believed to be 2.5 kg. In order to test this...
• 10M.3sp.hl.TZ0.2: The random variable X has a Poisson distribution with mean \(\mu \). The value of \(\mu \) is...
• 14N.3sp.hl.TZ0.5a: Find the critical region for this test.
• 14N.3sp.hl.TZ0.5c: It is now known that in the area in which the plant was found \(90\% \) of all the plants are of...
• 14N.3sp.hl.TZ0.5d: If, having done the test, the sample mean is found to lie within the critical region, find the...
• 15M.3sp.hl.TZ0.2b: (i)     State suitable hypotheses to test the claim that extra tuition improves examination...
• 18M.3sp.hl.TZ0.3a: State suitable hypotheses for a two-tailed test.
• 18M.3sp.hl.TZ0.3b: Find the critical region for testing \({\bar b}\) at the 5 % significance level.
• 18M.3sp.hl.TZ0.3c: Find the probability of making a Type II error.

Type I and II errors, including calculations of their probabilities.

• 12M.3sp.hl.TZ0.1b: In spite of these results the baker insists that his claim is correct. Stating appropriate...
• 08M.3sp.hl.TZ2.5: (a)     Find the appropriate critical regions corresponding to a significance level of   (i)    ...
• 09N.3sp.hl.TZ0.1: The mean weight of a certain breed of bird is believed to be 2.5 kg. In order to test this...
• 10M.3sp.hl.TZ0.2: The random variable X has a Poisson distribution with mean \(\mu \). The value of \(\mu \) is...
• 10N.3sp.hl.TZ0.4: A teacher has forgotten his computer password. He knows that it is either six of the letter J...
• 18M.3sp.hl.TZ0.3a: State suitable hypotheses for a two-tailed test.
• 18M.3sp.hl.TZ0.3b: Find the critical region for testing \({\bar b}\) at the 5 % significance level.
• 18M.3sp.hl.TZ0.3c: Find the probability of making a Type II error.

Testing hypotheses for the mean of a normal population.

• 12M.3sp.hl.TZ0.1b: In spite of these results the baker insists that his claim is correct. Stating appropriate...
• 08M.3sp.hl.TZ1.4: (a)     Calculate an unbiased estimate for   (i)     \(\mu \) ,   (ii)     \({\sigma ^2}\)...
• 08M.3sp.hl.TZ2.3: (a)     State appropriate null and alternative hypotheses. (b)     Test at the 5 % significance...
• 08M.3sp.hl.TZ2.5: (a)     Find the appropriate critical regions corresponding to a significance level of   (i)    ...
• 08N.3sp.hl.TZ0.2: The apple trees in a large orchard have, for several years, suffered from a disease for which the...
• 09M.3sp.hl.TZ0.2: (a)     After a chemical spillage at sea, a scientist measures the amount, x units, of the...
• 09N.3sp.hl.TZ0.1: The mean weight of a certain breed of bird is believed to be 2.5 kg. In order to test this...
• 10M.3sp.hl.TZ0.1: Anna cycles to her new school. She records the times taken for the first ten days with the...
• 14N.3sp.hl.TZ0.5a: Find the critical region for this test.
• 15M.3sp.hl.TZ0.2b: (i)     State suitable hypotheses to test the claim that extra tuition improves examination...
• 16N.3sp.hl.TZ0.1d: (i)     State the distribution of your test statistic (including any parameters). (ii)     Find...
• 16N.3sp.hl.TZ0.2d: Calculate the probability that he makes a Type II error.
• 17N.3dm.hl.TZ0.2a: Find an expression for \({u_n}\) in terms of \(n\).
• 18M.3sp.hl.TZ0.3a: State suitable hypotheses for a two-tailed test.
• 18M.3sp.hl.TZ0.3b: Find the critical region for testing \({\bar b}\) at the 5 % significance level.
• 18M.3sp.hl.TZ0.3c: Find the probability of making a Type II error.