Question

Two movie theaters are across the street from one another, in direct competition! Theater A takes a sample of 50 days, and finds that in that sample an average of 547 customers come through the theater each day, with a standard deviation of 42. They proudly display their results. Theater B takes a sample of 30 days and finds that in their sample, they have an average of 571 customers, with a standard deviation of 59. They claim this means they draw more customers than Theater A. The degrees of freedom for this situation is 4849.

a) Does this scenario represent a matched pairs or independent samples situation?

b) Construct a 95% confidence interval for difference in customers between Theater A and Theater B, and interpret.

c) You wish to see if Theater B’s claim is statistically significant at a significance level of .05. What are the hypotheses for an appropriate test?

d) Calculate the t-test statistic for the test defined in part (c).

e) Find the P-value for the test.

f) Make your conclusion for the hypothesis test and interpret its meaning in the context of the problem.

Answer 1

1- Theater A

2- Theater B

a)

this is independent sample

b)

95% CI = (-48.7605,0.7605)

c)

since 0 is present in confidence interval , Theater B’s claim is not statistically significant at a significance level of .05

Ho: mu1 = mu2

Ha: mu1 < mu2

d )

e)

p-value = P(t < TS)

= 0.0286

f)

since p-value < alpha, we reject the null hypothesis we conclude that Theater B’s claim is statistically significant at a significance level of .05