Question

The mean length of a small counterbalance bar is 43 millimeters. 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 = _______).

a) 5
b) 10
c) 15
d) 20

Answer 1

To test the claim that there has been no change in the mean length of the counterbalance bars, conduct a hypothesis test. The null hypothesis would be that the mean length is 43 millimeters, while the alternative hypothesis would be that there has been a change in the mean length. Use a t-test to compare the sample mean to the hypothesized mean and calculate the p-value.

Step-by-step explanation:

To test the claim that there has been no change in the mean length of the counterbalance bars, we can conduct a hypothesis test. The null hypothesis (H0) would be that the mean length is 43 millimeters, while the alternative hypothesis (Ha) would be that there has been a change in the mean length. We can use a t-test to perform the hypothesis test, since the population standard deviation is not given.

Given that we have 12 bars, the answer is (c) 15. The sample mean of 43 millimeters can be compared to the hypothesized mean of 43 millimeters to determine if there is enough evidence to reject the null hypothesis. Based on the test statistic and the critical value from the t-distribution table, we can calculate the p-value. If the p-value is less than the significance level of 0.02, we would reject the null hypothesis and conclude that there has been a change in the mean length.