The manager of a Piggly Wiggly grocery store claims a membership card will save consumers (through automatic discounts and extra coupons) at least $15.00 per week on average. To check this claim, a random sample of 11 shoppers with membership cards was obtained and their weekly grocery bills were inspected. The sample mean savings was x = $14.35 and s = $3.75. Assume the distribution of savings is normal.
a. Is there any evidence to refute the manager’s claim? Use a = 0.025.
b. If you rejected the null hypothesis, how can you explain this conclusion when $14.35 is so close to $15.00? If you did not reject the null hypothesis, how can you explain this conclusion when $14.35 is certainly less than $15.00?
c. Find bounds on the p value associated with this hypothesis test.
Lionfish are native to Indo-Pacific waters but were introduced into the Atlantic in the 1990s. These spiney fish have huge appetites, feed on native species, and have a mean length of 13.5 inches.45 Recently, invasive lionfish were found 300 feet below the water’s surface off the coast of Florida. There was some speculation that these fish were larger than previously observed. A random sample of 24 lionfish was obtained near the sunken Bill Boyd cargo ship close to Fort Lauderdale, and the length of each was recorded (in inches). The summary statistics were x = 16.005 and s = 4.039.
a. Is there any evidence to suggest that the true mean length of lionfish in this area near Fort Lauderdale is greater than 13.5 inches? Use a = 0.01 and assume the underlying population is normal.
b. Find bounds on the p value associated with this test.