Question

A travel agency wishes to publish a new brochure claiming that its customers on average give it at least 9 out of 10 for holiday satisfaction. It conducts a sample of 40 customers, and finds that sample mean level of satisfaction is 9.1. The sample standard deviation is 0.5.

(a) What distribution should you use when testing the travel agency’s claim? Give a reason for your answer
(b) Does the sample support the agency’s claim at the 5% level?

Answer 1

A t-distribution is used because the sample size is small and the population standard deviation is unknown. A one-sample t-test is conducted to see if the sample supports the travel agency's claim at the 5% level, but actual calculations are needed to determine this definitively.

Step-by-step explanation:

When testing the travel agency's claim regarding holiday satisfaction scores, the appropriate distribution to use is a t-distribution. This is because the sample size is less than 30, and the population standard deviation is unknown. In testing at the 5% significance level (alpha = 0.05), the t-distribution provides a way to account for increased variability that comes with estimating the population standard deviation using a small sample.

To determine whether the sample supports the agency's claim at the 5% level, a one-sample t-test is conducted. If the t-statistic calculated falls within the critical values for a t-distribution with n-1 degrees of freedom, and the p-value associated with the t-statistic is greater than 0.05, the null hypothesis that the mean satisfaction score is less than or equal to 9 is not rejected. In this case, the sample would support the agency's claim. However, the actual calculations, including the resulting t-statistic and p-value, should be provided to make a definitive statement on support for the claim. Without these calculations, we cannot conclude the level of support the sample provides for the claim.