Sixteen randomly chosen people suffering from excess weight are placed on a year

Question

Sixteen randomly chosen people suffering from excess weight are placed on a year-long exercise regimen and their weights before and after are compared. The claim is that this exercise regimen will allow participants to lose an average of at least 20 lbs in a year. After one year, the weight losses for each participant were measured. The sample data were plotted and found to follow an approximately Normal distribution with no outliers. The average weight loss in this group was 24.7 lbs. with a sample standard deviation of 12.4 lbs.

1: Explain the circumstances under which it is appropriate to use a z-procedure and under which circumstances one should use a t-procedure. What is the appropriate procedure to use in this case?

Please show all work and explain your answer.

Explanation / Answer

1. z-procedure is used when n>30 and t is used when n<30

For this case n=16<30, so we will use t-procedure

Find t statistics, compare it will p value and make the decision

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