2. The manager of a Kroger grocery store claims a membership card will save consumers more than $15 per week on average. To check this claim, a random sample of 16 shoppers with membership cards was obtained and their weekly grocery bills were inspected. Suppose the sample mean was $16.35 and the sample standard deviation was $3.40. Assume the distribution of savings is normal. a. Check the necessary assumptions and conditions for doing this test. b. What are the appropriate hypotheses to test the claim? c. Calculate the appropriate test statistic and p-value. d. What is the conclusion? 3. According to an annual survey conducted by TheKnot.oom, the mean cost of a wedding in 2017 was $33,391 (yikesl). Suppose the cost for a wedding is normally distributed, with a population standard deviation of $1500, and a wedding is randomly selected. a. What is the probability a randomly selected wedding costs more than $35,000? b. Suppose a random sample of 16 weddings is taken. What is the probability that the average cost is greater than $34,000? 4. According to the U.S. Fire Administration, approximately 25,000 res are caused by reworks each year in the United States. Despite numerous public warnings against the use of reworks, the home property damage due to these res is enormous. In a random sample of 55 res due to reworks, the resulting mean property damage was $840.25. The sample standard deviation is $320.25. Assume property damage due to reworks is normally distributed. Calculate a 95% condence interval for the true mean property damage due to a re caused by reworks. Make sure to check appropriate conditions and to interpret your interval in context