Stating null and alternative hypotheses, carry out an appropriate test at the 5 % level to decide whether the farmer’s claim can be justified.

State the name of this test for validity.

State the name of this test for reliability.

State a possible disadvantage of using this test for reliability.

In order to test for the goodness of fit, the test statistic was calculated to be 1.0847. Show how this was done.

Hence determine, with a reason, if the new exam is a valid indicator of future performance.

Calculate Pearson’s product moment correlation coefficient for this data.

A different horse breeder collected data on the time and outcome of births. The data are summarized in the following table:

Carry out an appropriate test at the 5% significance level to decide whether there is an association between time and outcome.

Hence determine, with a reason, if the survey is reliable.

Find the standard deviation of the changes.

If you were to repeat the test performed in part (e) intending to compare the quality of the teaching between the two schools, suggest two ways in which you might choose your sample to improve the validity of the test.

State why comparing only the final IB points of the students from the two schools would not be a valid test for the effectiveness of the two different teaching methods.

Use an appropriate test to determine whether showing an improvement is independent of gender.

State why it was important to test that both sets of points were normally distributed.

Write down appropriate hypotheses.

Carry out a test at the 1% significance level, and state your conclusion.

Test, at the 5% level of significance, whether or not the data can be modelled by a Poisson distribution.

The number of cars passing a certain point in a road was recorded during 80 equal time intervals and summarized in the table below.

Carry out a ${\chi }^2$ goodness of fit test at the 5% significance level to decide if the above data can be modelled by a Poisson distribution.

Calculate the value of the ${\chi }^2$ statistic and state your conclusion using a 10% level of significance.

The data from the two samples above are combined to form a single set of data. The following frequency table gives the observed frequencies for the combined sample. The data has been divided into five intervals.

Test, at the 5% level, whether the combined data can be considered to be a sample from a normal population with a mean of 380.

A horse breeder records the number of births for each of 100 horses during the past eight years. The results are summarized in the following table:

Stating null and alternative hypotheses carry out an appropriate test at the 5% significance level to decide whether the results can be modelled by B (6, 0.5).

Calculate an appropriate value of ${\chi }^2$ and state your conclusion, using a 1% significance level.

State suitable hypotheses.

State suitable hypotheses for testing this belief.

Identify a test that might have been used to verify the null hypothesis that the predictions from the standardized test can be modelled by a normal distribution.

the level of significance of a hypothesis test.

Find the mean and standard deviation of the sample data in the table above. Show how you arrived at your answers.

Find the mean change.

Hence estimate $p$, the probability that a randomly chosen egg is brown.

Hence, find the expected improvement between predicted and final points for an increase of one unit in effort grades, giving your answer to one decimal place.

By calculating an appropriate ${\chi }^2$ statistic, test, at the 5% significance level, whether or not the binomial distribution gives a good fit to these data.

Without doing any further calculations, explain briefly how you would carry out a test, at the 5% significance level, to decide if the data can be modelled by B(6, $p$), where $p$ is unspecified.

Use an appropriate test to determine whether there is evidence, at the 5 % significance level, that the students in school B have improved more than those in school A.

Calculate unbiased estimates of the population mean and the population variance.

Find the significance level of this procedure.

Find the exact value of the mean of this distribution.

Some time later, the actual value of $\mu$ is 503. Find the probability of a Type II error.

Show that this data leads to an estimated value of $p=0.4$.

Use a paired $t$-test to determine whether there is significant evidence that the students in school A have improved their IB points since the start of the course.

Describe one way in which Juliet could improve the reliability of her investigation.

Describe one criticism that can be made about the validity of Juliet’s investigation.

The scientists wish to investigate the claim that Group B gain weight faster than Group A. Test this claim at the 5% level of significance, noting which hypothesis test you are using. You may assume that the weight gain for each group is normally distributed, with the same variance, and independent from each other.

Calculate the mean of these data and hence estimate the value of $p$.

a goodness of fit test (a complete explanation required);

State the name of this type of test for reliability.

Calculate the mean number of eggs laid by these birds.

Most of the expected frequencies have been calculated in the third column. (Frequencies have been rounded to the nearest integer, and frequencies in the first and last classes have been extended to include the rest of the data beyond 15 and 225. Find the values of $a$, $b$ and $c$ and show how you arrived at your answers.

Calculate the mean number of brown eggs in a box.

Perform a test on the data from school A to show it is reasonable to assume a linear relationship between effort scores and improvements in IB points. You may assume effort scores follow a normal distribution.

State your hypotheses, critical number, decision rule and conclusion (using a 5% level of significance).