Walmart conducted a study in 2017 on the amounts customers spent at their stores in Shenzhen on the day of New Year’s Eve. The amounts were found to be normally distributed, with an average of ¥1,800 and a standard deviation of ¥240.

In 2018, Walmart suspected that the average amount had increased. A hypothesis test was conducted at a significance level of 5% to test the suspicion. A random sample of size 179 was selected with mean ¥1,850 and standard deviation ¥390.

1: Assume that the population standard deviation had not changed from 2017. Find the test statistic.

2: Based on the assumption in Question 1 above, find the rejection region.

3: Based on the assumption in Question 1, find the p-value.

4: What are the conclusions?

5: The assumption made in Question 1 was certainly not reasonable. Find the test statistic again, assuming that the population standard deviation had changed from 2017.

6: Find the rejection region again based on the new assumption made in Question 5.

It was also found that in the above sample, about 19% of the amounts are above ¥2,400. A hypothesis test was then conducted to test if less than 20% of SZ customers spent more than ¥2,400 on the day of New Year’s Eve, at α = 2.5%.

7: Find the test statistic.

8: Find the rejection region.

9: What are the conclusions?