Inferential Statistics & Probability Worksheet

A surprising number of people are scared of clowns. You expect that people will have more nightmares the night that they see clowns at the circus. To test this, you send a group of people to a circus with clowns, and a group to a circus without clowns, and measure the number of people in each group who have nightmares that night. Your data is shown below:


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Nice dreams

No clowns






Perform a Z

test on nightmares after the no-clown circus minus nightmares after the clown circus. Report the test statistic.

A lot of people were scared of clowns after seeing the horror movie IT about a killer clown. However, perhaps seeing a regular clown at the circus reduces this fear.

We examine two groups of people who have seen the movie ‘IT’, one group has been to the circus since seeing the film and one group has not. In the group that has been to the circus, the proportion of clown phobia is 0.016. In the group that has not been to the circus, the proportion of clown phobia is 0.034.

Calculate the relative risk of clown phobia if you don’t go to the circus after seeing the film ‘IT’.

In your sample of 23 art students and 30 economics students, the mean amount that a group of economics students like statistics is 26, while the mean amount that a group of art students like statistics is 15. The variance in the economic group is 4.2, while the variance in the art group is 10.3.

Calculate your test statistic for finding whether the groups differ in how much they like statistics.


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