1. Your average weekly grocery bill at the store you usually shop is $300. You decided to test a new strategy of buying most items over the weekend from Costco in bulk and when you fall short of some items during the week or the once not appropriate for Costco, you buy from a convenience store near you. You took a sample of your expenses for 20 weeks and found that the average is $285 and the standard deviation for the sample is $25. Set up your null and alternative hypothesis for testing whether your cists are different and do the analysis using α=.05.

2. You started a new restaurant. Based on invoices for the first 30 days, you estimated your average grocery bill to be $20,000 with a standard deviation of $2000. You want to start another restaurant in a similar neighborhood and you are planning to prepare a brochure for investors and to work out a deal with a whole sale food distributor. Prepare a 95% confidence interval for the average grocery bill. Would a 99% confidence interval be narrower or wider than the 95% confidence interval?

3. You move to a new town and want to decide on when to start for work. You do not want to reach too early and not be too late too many times. You, thus, collected data for 10 days and obtained an average of 34.5 minutes. You took the standard deviation of 4.5 minutes from a commuting friend and believe that that is the standard deviation for the area. Prepare a 95% confidence interval for the true average commuting time.