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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 weigh 155 lbs on 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?
(b) What are your null and alternate hypotheses? In plain English, explain what are your type I and type II errors in this case?
(c) Would you reject your null hypothesis at the 5% level? How about the 10%, 2%, and 1% levels?
(d) In the example above, suppose the margin of error (how many percentage points your sample differs from the population) is 0.8 and the investigator plans to use the 80% confidence interval. Determine the minimum sample size required in this case.
Hint: Refer to how confidence interval is calculated and how sample size determines the confidence interval.
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