Question

A reporter estimates that professional golfers have an average height of 70.1 inches, with a variance of 7.17. To test this estimate, a researcher chooses a random sample of 22 professional golfers and finds that their mean height is 70.2 inches, with a variance of 10.40. Do these data provide enough evidence, at the 0.1 level of significance, to reject the claim that the true variance, σ2, of professional golfers' heights is equal to 7.17? Assume that the heights of professional golfers are approximately normally distributed.Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.1 level of significance: (Round to at least three decimal places.) and Can we reject the reporter's estimate that the variance of professional golfers' heights is equal to 7.17? Yes No

Answer 1

H₀: = 7.17

H₁: 7.17

The test statistic

                                 

                                 

The critical values are

                                  

No, we cannot reject the reporter's estimate that the variance of professional golfer's heights is equal to 7.17. Because the test statistic value lies between the critical values(11.5913 < 30.4603 < 32.6706).