Question

A contractor claims the mean value of his compression test is 6500 psi and has astandard deviation of 500 psi. You attempt to check this by taking 8 sample measurements and findyour average is 5900 psi. If your levelof significance is 0.01, would you believe the means are the same

Answer 1

This value of 5675 psi by the contractor is safer than 5487.5 psi as it is of lesser value.

Explanation:

The following parameters are given from the question above. These information is used in solving this problem.

=> The mean value of his compression test = 6500 psi, the standard deviation = 500 psi, the average of the mean = 5900 psi and the number of sample measurements = 8.

The first thing to do right now is to determine the characteristic strength, this can be calculated as below:

Characteristic strength= average of the mean - (1.65/2) × standard deviation.

Characteristic strength = 5900 - (0.825) × 500 = 5487.5 psi.

The next thing to do is to Determine the target mean strength.

Target mean strength = 5487.5 psi + 1.65 × 500 = 6312.5 psi.

The above is from taking samples from 8 samples.

Now, let's consider the characteristic strength by the contractor.

Characteristics strength = 6500 - 165 × 500 = 5675 psi.

This value of 5675 psi by the contractor is safer than 5487.5 psi as it is of lesser value.