Question

A simple random sample of 8 women basketball player’s weights have a standard deviation of 7.5 lb. Find the test statistic, using a 0.05 significance level, to test a claim that the standard deviation of all weights of women basketball players is less than 9 lb. Could anyone show me how to do this?

Answer 1

Standard error=7.5/√8=2.6517lb approx. The critical value for 95% confidence level (0.05 significance level) is 1.895 for 8-1=7 degrees of freedom (1-tail). The margin of error is 1.895×2.6517=5.02lb approx. This is a 1-tailed critical value because we are testing for less than 9lb, not less than or greater than. The upper limit of the margin of error in the sample is 12.52lb, which exceeds 9lb. The lower limit is 2.48lb. So I think it’s uncertain that the standard deviation is less than 9lb.