Your company sells exercise clothing and equipment on the Internet. To design th

Question

Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. Here are the weights (in kilograms) for a sample of 24 male runners. Assume that these runners can be viewed as a random sample of your potential male customers. Suppose also that the standard deviation of the population is known to be sigma = 3.5 kg 55 58.8 58.5 53.9 57.2 65.8 59 59.5 69.9 61.3 58.4 62.5 61.9 53.6 56.7 53 60.9 58.1 63.2 59.3 61.6 57.4 59.7 59.5 (a) What is sigma_x, the standard deviation of X? (b) Give a 95% confidence interval for mu, the mean of the population from which the sample is drawn. (c) Will the interval contain the weights of approximately 95% of similar runners? Explain your answer. No, this interval pertains to the average weight, not the weights of individual runners. Yes, it will contain the weights of approximately 95% of similar runners. The term confidence level refers to: a. the absolute number of interval estimates that can be expected to contain the actual value of the parameter being estimated when the same procedure of interval construction is used again and again b. the percentage of interval estimates that can be expected to contain the actual value of the parameter being estimated when the same procedure of interval construction is used again and again c. the range of values among which an unknown population parameter can presumably be found d. the sum of an estimators squared bias plus its variance, which indicates the degree to which it is consistent, efficient, and unbiased e. both (b) and (c)

Explanation / Answer

a) excel function: =STDEV.S(A1:A24)

answer: 3.826

b) excel function for margin of error: =CONFIDENCE.T(0.05, 3.826, 24) -> 1.6156
excel function for average: =AVERAGE(A1:A24) -> 59.3625
95% CI = (57.75, 60.98)

c) No, this interval pertains to the average weight, not the weights of individual runners

d) b. the percentage of interval estimates that can be expected to contain the actual value of the parameter being estimated when the same procedure of interval construction is used again and again

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