Question

Katie works in the film industry and was interested in knowing whether people go to the movies more often in the summer than they do in the winter (assume these data were collected prior to the current pandemic). She collected data from ten people, asking each of them to report how many movies they had gone to the previous summer, and then followed up with them later that year to find out how many movies they went to that winter. Her data are recorded below:

Summer: 5,2,5,4,6,3,7,5,5,6
Winter: 5,3,3,4,4,2,4,4,3,4

a.) Conduct the appropriate test of hypothesis, using α = .05.

b.) Generate a 95% confidence interval for these data

c.) if you instead generated a 90% confidence interval, what would happen to the interval? (1 mark). Why? (1 mark)

Answer 1

( a )

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that   people go to the movies more often in the summer than they do in the winter at the 0.05 significance level.

( b )

= ( 0.071 , 2.329 )

( c )

As the confidence level decreases from 95 % to 90% the width of the interval decreases