The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting 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 in millimeters recorded. The lengths (in millimeters)are 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 is 1.784. If the 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 of -2.913 with the critical t-value at the 0.02 level of significance with 11 degrees of freedom. The critical t-value in this case is -2.718. Since the computed t-value is smaller (further to the left) than the critical t-value, we reject the null hypothesis at the 0.02 level of significance. Therefore, we can conclude that there has been a statistically significant change in the mean length of the bars.

The Mean Length of a Candy Bar Is 43 Millimeters