1. Before the implementation of a new scanning procedure, the average time to check out a supermarket customer was 5.6 minutes. When a random sample of 120 customers was observed with the new procedure, the checkout times had an average of 5.0 minutes with a standard deviation, s = 2.3 minutes. Can we conclude that the new procedure requires less time than the previous method? Use = .01.

2.In computing total payload weight, an airline has been using the figure of 45 pounds for the average weight of carry-on luggage of passengers. In a recent sample of 600 passengers, the carry-on luggage weights were found to have a mean of 46.3 pounds and a standard deviation of 20 pounds. Can the airline conclude that the mean carry-on weight is no longer 45 pounds? Use = .05. What is the p-value of this test?

3. For problem 1, state the rejection rule in terms of X-bar(crit) rather than z(crit).

4.For problem 2, state the rejection rule in terms of X-bar(crit) rather than z(crit).

5.For problem 1, estimate the power under the specific alternative hypothesis H1: mu = 5. You may use the methods demonstrated in the lecture, or use a web-based calculator, such as: https://www.stat.ubc.ca/~rollin/stats/ssize/n1.html

6.For the same example, what N would be needed in a replication study to achieve a power of approximately 80%? [HINT: trial-and error, trying different N's is one easy approach that can be done by hand. Or a web-based calculator may facilitate doing this directly.]

I need help solving these large-sample problems. This is all the information I was given by my instructor. I'd appreciate step-by-step explanations thank you!!