Question: Judy Povich is a fashion designer artist who designes the display windows in front of a large clothing store in New York City. Electronic counters at the entrances total the number of people entering the store each business day. Before Judy was hired by the store, the mean number of people entering the store each day was 3218. However, since Judy has started working, it is thought that this number increased. A random sample of 42 business days after Judy began work gave an average \(\bar{X}\) = 3392 people entering the store each day. The sample standard deviation was s = 287 people. Does this indicate that the average number of people entering the store each day has increased? Use a 1% level of significance.

(a) What is the null hypothesis? What is the alternate hypothesis? Will we use a left-tailed, right-tailed, or two-tailed test? What is the level of significance?

(b) What sampling distribution will we use? What is the critical value zo (or critical values ± zo)

(c) Sketch the critical region and show the critical value (or critical values).

(d) Calculate the z value corresponding to the sample statistic \(\bar{X}\) and show it’s location on the sketch of part (c)

(e) Based on your answers for parts (a) to (d), shall we reject or fail to reject (i.e., “accept”) the null hypothesis at the given level of significance \(\alpha \) ? Explain your conclusion in the context of the problem.

(f) Are the data statistically significant?