Golf Averages: A study of 35 golfers showed that their average score on a partic

Question

Golf Averages:    A study of 35 golfers showed that their average score on a particular course was 92. The standard deviation of the sample is 5. a) Find the best point estimate of the mean. b) find the 95% confidence interval of the mean score for all golfers. c) find the 95% confidence interval of the mean score if a sample of 60 golfers is used instead of a sample of 35. d) which interval is smaller? explain why. Thank you Golf Averages:    A study of 35 golfers showed that their average score on a particular course was 92. The standard deviation of the sample is 5. a) Find the best point estimate of the mean. b) find the 95% confidence interval of the mean score for all golfers. c) find the 95% confidence interval of the mean score if a sample of 60 golfers is used instead of a sample of 35. d) which interval is smaller? explain why. Thank you

Explanation / Answer

a) The best point estimate of the mean is the mean of the sample so here it is 92. b) formula is xbar +- t* s/n^0.5 where xbar is the sample mean, t* is the critical value (2.04 for a 95% confidence interval with 34 (n-1)degrees of freedom), s is the standard deviation of the sample, and n is the sample size. We use a t distribution here because the standard deviation of the population is unknown. So we have 92+- 1.72 (90.28, 93.72). c. If the sample size is 60 we get 92+- 2.0 *5/60^.5= 92+-1.29 (90.71, 93.29). d With a larger sample size we have a tighter sampling distribution, so the confidence interval is smaller.

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