Question: Children in the United States account directly for $36 billion in sales annually. When their indirect influence over product decisions from stereos to vacations is considered, the total economic spending affected by children in the United States is $290 billion. It is estimated that by age 10, a child makes an average of more than five trips a week to a store (M. E. Goldberg, G. J. Gorn, L. A. Peracchio, and G. Bamossy, Understanding Materialism Among Youth, Journal of Consumer Psychology, 2003, 13(3) pp. 278 288). Suppose that you want to prove that children in your city average more than five trips a week to a store. Let represent the population mean number of times children in your city make trips to a store.
a. State the null and alternative hypotheses.
b. Explain the meaning of the Type I and Type II errors in the context of this scenario.
c. Suppose that you carry out a similar study in the city in which you live. Based on past studies, you assume that the standard deviation of the number of trips to the store is 1.6. You take a sample of 100 children and find that the mean number of trips to the store is 5.47. At the 0.01 level of significance, is there evidence that the population mean number of trips to the store is greater than 5 per week?
d. Interpret the meaning of the p-value in (c).