Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use the critical value method of testing hypothesis. a. The Stewart Aviation Products Company uses a new production method to manufacture aircraft altimeters. A simple random sample of 81 altimeters is tested in a pressure chamber, and the errors in altitude are recorded as positive values (for readings that are too high) or negative values (for readings that are too low). The sample has a standard deviation of s = 52.3 ft. At the 0.05 significance level, test the claim that the new production line has errors with standard deviation different from 43.7 ft, which was the standard deviation for the old production method. If it appears that the standard deviation has changed, does the new production method appear to be better or worse than the old method?

We need to compare the sample standard deviation of 52.3 to the known population standard deviation of 43.7. The test we will use will use Chi-Square distribution...

The hypothesis for this test are...

H0: σ = 43.7

Ha: σ ≠ 43.7

This is a 2 tailed test.

We have n = 81

s = 52.3

s² = 52.3² = 2735.29

σ = 43.7

σ² = 1909.69

The degrees of freedom are: n - 1, in this case, 80

Our significance level is 95%, so our critical values are

Χ² < 57.153 and Χ² > 106.629

The test static is found with the formula:

Χ² = [(n - 1)s²]/σ²

Plug in what we have and find the test stastic....

Χ² = [80(2735.29)]/1909.69

Χ² = 114.586

114.586 > 106.629, we reject the null hypothesis. There is evidence that shows that the standard deviation has changed. The evidence suggests that it has increased, which would make the new method worse than the old method.