1. Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco's rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $135.25.
Assume that the population standard deviation is $10.50 and that spending follows a normal distribution.
a) Specify the appropriate null and alternative hypotheses to test whether average spending at the rival's store is more than $130.
b) Run both a critical value and p-value test at the 5% significance level.
2. An article in the National Geographic News (February 24, 2005) reports that Americans are increasingly skimping on their sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes the average sleep time of 6.7 hours on weekdays. Assume that the population is normally distributed with a known standard deviation of 2.1 hours.
a) Specify the null and alternative hypotheses.
b) Run a critical value and p-value hypothesis test at 1% level of significance.