Final Answer:
A two-tailed hypothesis test should be performed to determine if the mean pipe length is 13 inches. The test statistic is the z-score, and there is sufficient evidence at the α=0.01 significance level to support the technician's claim.
Explanation:
A two-tailed hypothesis test should be performed in this case to determine if the mean pipe length is 13 inches. The two-tailed hypothesis test is used when the claim being tested is two-sided, meaning that it can be either greater or less than the value given. In this case, the technician is claiming that the mean pipe length is not 13 inches, so this is a two-sided claim.
The test statistic for this hypothesis test is the z-score. This is calculated by subtracting the sample mean (13.06) from the population mean (13), and then dividing by the standard deviation of the sample (0.11). This gives us a z-score of 0.55.
We can then use the z-score to determine if there is sufficient evidence at the α=0.01 significance level to support the technician's claim. To do this, we look at a z-table to determine the corresponding area (p-value) for the given z-score of 0.55. This gives us a p-value of 0.2917, which is greater than α=0.01. This means that there is not sufficient evidence at the given significance level to reject the null hypothesis, which states that the mean pipe length is 13 inches. Therefore, we can conclude that there is sufficient evidence at the α=0.01 significance level to support the technician's claim that the mean pipe length is not 13 inches.