Question

The thicknesses of eight pads designed for use in aircraft engine mounts are measured. The results, in mm, are 41.83, 41.01, 42.68, 41.37, 41.83, 40.5, 41.70, and 41.42. Assume that the thicknesses are a sample from an approximately symmetric distribution.

a. Compute the appropriate test statistic and find the P-value.

b. Can you conclude that the mean thickness is greater than 41 mm?

c. The target thickness is 42 mm. Can you conclude that the mean thickness differs from the target value? Compute the appropriate test statistic and find the P-value.

Answer 1

a) From the given data

Statistics Total Sum of Variable Count Mean StDev Variance Sum Squares Data 8 41.543 0.644 0.414 332.340 13809.134

The Z-statistic is computed as follows: X - μo 41.543 – 41 0.644/18 2.385 o/vn

Using the P-value approach: The p-value is p = 0.0085

b) Since P-value < alpha 0.05 so we reject H0

Thus we conclude that the mean thickness is greater than 41 mm

c) Test Statistic:

The Z-statistic is computed as follows: X - HO 2= 41.543 - 42 0.644/V8 -2.007 o/Vn

Using the P-value approach: The p-value is p = 0.0447

since P-value < alpha 0.05 so we reject H0

Thus we conclude that the mean thickness is not equal to 42 mm