The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments 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 area beyond the critical.
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.

Question

Quizplus · Accepted Answer

To test the claim at the 0.02 level, we need to compare the computed t-value with the critical t-value with 11 degrees of freedom (n-1) at the 0.01 level (two-tailed test). From the t-distribution table, the critical t-value is ±3.106. Since -2.913 lies in the area beyond the critical (-3.106), we reject the null hypothesis and conclude that there has been a statistically significant change in the mean length of the bars at the 0.02 level. Therefore, the correct choice is A.

The Mean Length of a Small Counter Balance Bar Is