The mean length of a small counter balance bar is 43 millimeters. There is concern that the settings of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and the standard deviation 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?
A) Yes, because the computed t lies in the rejection region.
B) No, because the information given is not complete.
C) No, because the computed t lies in the area to the right of -2.718.
D) Yes, because 43 is greater than 41.5.

Question

Quizplus · Accepted Answer

We need to compare the computed t-value (-2.913) with the critical t-value for a two-tailed test at the 0.02 level with df = 11 (n-1). Using a t-table or calculator, the critical t-value is approximately ±2.718. Since the computed t-value (-2.913) lies in the rejection region (to the left of -2.718 and to the right of +2.718), we reject the null hypothesis and conclude that there is a statistically significant change in the mean length of the bars. Therefore, the best choice is A.

The Mean Length of a Small Counter Balance Bar Is