The weights of 121 31-year-old adults randomly selected from the are normally distributed with a mean of 160 lbs.It is known that 31-year-olds weight 155 lbs on an average with a standard deviation of 5 lbs.

You want to test the statement: "The sample is heavier than an average 31-year-old adult"

(a)Do you use a one-tailed or a two-tailed test? Why? (0.5 Points)

(b)What are your null and alternate hypotheses? In plain English, explain what are your type I and type II errors in this case? (1 Point)

(c)Would you reject your null hypothesis at the 5% level? How about the 10%, 2% and 1% levels? (2 points)

(d)In the example above, suppose themargin of error (how many percentage points your sample differs from the population) is 0.8 and investigator plans to use the 80% confidence interval. Determine the minimum sample size required in this case. (1.5 points)

Hint: Refer to how confidence interval is calculated and how sample size determines the confidence interval.