Question

You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms: 67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9 60.9 69.2 63.7 68.3 64.7 65.6 56.0 57.8 66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7 a) Suppose that the standard deviation of the population is known to be sigma = 4.5 kg. What is sx, the standard error of x? b) Give a 95% confidence interval for the mean of the population from which the sample is drawn. c) Are you quite sure that the average weight of the population of runners is less than 65 kg?

Answer 1

a) Suppose that the standard deviation of the population is known to be sigma = 4.5 kg. What is sx, the standard error of x?

δx = δ/√n = 4.5kg / √24 = 4.5kg / 4.90 = 0.918

b) Give a 95% confidence interval for the mean of the population from which the sample is drawn.
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x + z * δ/√n  where z* = 1.96 for the 95% confidence interval

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x  = Σx / n = 1483/24 = 61.79

61.79 + 1.96(0.918) = between 59.99 kg and 63.59 kg

c) Are you quite sure that the average weight of the population of runners is less than 65 kg?
Based on my computation, 65 kg is above the 95% confidence interval.  Thus, the average weight of the population of runners is less than 65 kg.