Question

A manufacturing company makes aircraft altimeters.   These devices are tested in a pressure chamber,
and errors in altitude are recorded as either positive (for readings that are too high) or negative (for readings
that are too low).   Using a long established production method, the errors for these devices were normally
distributed with a standard deviation of 47.3 ft.

Now, a new production method is to be used; however, there is some concern that the new method produces
less accurate altimeters. To test this claim, a simple random sample of 81 altimeters is tested and the sample
has a standard deviation of s = 52.3 ft.  

Use this sample data and a significance level of ? =.05 to test the claim that the new production line has
errors with a standard deviation that is higher than 47.3 ft.

Answer 1

here null hypothesis: Ho: <=47.3

alternate hypothesis:Ha: >47.3

degree of freedom =n-1=81-1=80

for 80 degree of freedom and 0.05 level with right tailed test rejection region >101.88

here test statistic =(n-1)s²/² =(81-1)*(52.3/47.3)² =97.81

as test statistic is nt in rejection region we can not reject null hypotheiss

we do not have sufficient evidence at 0.05 level to conclude that  new production line has errors with a standard deviation that is higher than 47.3 ft