Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. Required:
a. Construct a 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period.
b. Explain in a complete sentence what the confidence interval means

a. The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. Explain in a complete sentence what the confidence interval means

It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

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step-by-step explanation: