Question

Example of appropriate t test

Answer 1

Following is an example of a right tailed, one sample t-test.

An engineer measured the Brinell hardness of 25 pieces of ductile iron that were subcritically annealed. The resulting data set was as given below:

170	167	174	179	179
156	163	156	187	156
183	179	174	179	170
156	187	179	183	174
187	167	159	170	179

The engineer hypothesized that the mean Brinell hardness of all such ductile iron pieces is greater than 170. Therefore, he was interested in testing the hypotheses:

H₀ : μ = 170
H_A : μ > 170

The level of significance is alpha = 0.05. Since the population standard deviation is not known to us, we are to use the sample standard deviation in its place.
The test statistic for our test will be of the form,

Here,

Therefore, T = 1.22

p-value =

Since p-value is greater than alpha = 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence, at the alpha = 0.05 level, to suggest that the mean Brinell hardness of all such ductile iron pieces is greater than 170.