Question

Question 6 5 pts A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of dress is designed to be 26 inches. The company regularly tests the lengths of the garments to ensure quality control, and if the mean length is found to be significantly longer or shorter than 26 inches, the machines must be adjusted. The most recent simple random sample of 28 dresses had a mean length of 26.30 inches with a standard deviation of 0.77 inches. Perform a hypothesis test on the accuracy of the machines at the 0.01 level of significance. Ho: Hai t-Test Statistic (round to three decimal places) - Critical t-score (it should be always positive): ta Conclusion (write "R" for reject Ho, and "F" for fail to reject Ho):

Answer 1

The provided sample mean is X = 26.3 and the sample standard deviation is s = 0.77, and the sample size is n=28. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: = 26 Ha: u 726 This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided the significance level is a = 0.01, and the critical value for a two-tailed test is to = 2.771. The rejection region for this two-tailed test is R={t: 1t| > 2.771} (3) Test Statistics The t-statistic is computed as follows: X - HO = 26.3 - 26 0.77/28 2.062 s/n (4) Decision about the null hypothesis Since it is observed that t = 2.062 <tc = 2.771, it is then concluded that the null hypothesis is not rejected.

please like ??