A university conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.8% of the 456 members of a fitness association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) 1. Which distribution should you use for this problem? (Round your answers to four decimal places.)

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The Student'st-distribution should be used because: Choose one answer

1. The Student'st-distribution should be used because square?npq ?10, which implies a small sample.

2. The standard normal distribution should be used because we are interested in proportions.

3. The Student'st-distribution should be used because we do not know the standard deviation.

4. The binomial distribution should be used because the two outcomes are "the runner died" and "the runner did not die.

2.

Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period. (i) State the confidence interval. (Round your answers to four decimal places.) () (ii} Sketch the graph. %"=E CL=_C_1 =E ) ] * (i) Calculate the error bound. (Round your answer to four decimal places.) L]