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 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

Based on the given information, we can conduct a one-sample t-test with the null hypothesis that the population mean length of the bars is still 43 millimeters and the alternate hypothesis that it has changed. Using a two-tailed test and a significance level of 0.02, the critical t-values are -2.681 and 2.681 (from a t-distribution with 11 degrees of freedom). Since the computed t-value of -2.913 falls in the rejection region (to the left of -2.681), we reject the null hypothesis and conclude that there has been a statistically significant change in the mean length of the bars. Therefore, the correct answer is A.

The Mean Length of a Small Counter Balance Bar Is