Question

A simple random sample consists of 65 lengths of piano wire that were tested for the amount of extension under a load of 30 N. The average extension for the 65 lines was 1.104 mm and the standard deviation was 0.030 mm. Let μ represent the mean extension for all specimens of this type of piano wire.

a)Find the P-value for testing H0 : μ ≤ 1.1 versus H1 : μ > 1.1. Round the answer to four decimal places.

b)Either the mean extension for this type of wire is greater than 1.1 mm, or the sample is in the most extreme ( ) % of its distribution. Round the answer to two decimal places.

Answer 1

The formula for the test statistic is:

X-bar = 1.104

s = 0.030

n = 65

Hence, t = (1.104 - 1.1)/(0.030/√65) = 1.08

The p-value associated with t = 1.08 and df = n - 1 = 64 is 0.1421

b) The question is not clear but we can definitely conclude that we do not reject the null hypothesis. We say that the mean extension for this type of wire is not greater than 1.1 mm. The sample is in the most extreme 14.21% of its distribution.