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 recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. 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

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 recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. 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.

Quizplus · Accepted Answer

We need to test the null hypothesis that the mean length is 43 mm against the alternative hypothesis that it is not equal to 43 mm.
The computed t-value is -2.65, which lies in the rejection region defined by a two-tailed test with 10 degrees of freedom at the 0.02 significance level. Therefore, we reject the null hypothesis and conclude that there has been a statistically significant change in the mean length of the candy bars.

The Mean Length of a Candy Bar Is 43 Millimeters