Question

7. A company manufactures altimeters. A simple random sample of 81 altimeters is tested in a pressure chamber, and the errors in altitude are found to have a standard deviation of 52.3 ft. At 0.05 significance level, test the claim that the production line has a standard deviation different from 43.7 ft.

Answer 1

null hypothesis:     Ho:				σ =	43.7
Alternate hypothesis: Ha:				σ ≠	43.7

for 5 % level and given df critical values of F      =			80.126		&	106.629
Decision rule:reject Ho if test statistic X2 in critical region:			80.126		< X2 >	106.629

test stat :

=χ2=(n-1)s2/σ2=

114.59

as test statistic is in critical region we reject null hypothesis. we have sufficient evidence at 0.05 level to conclude that production line has a standard deviation different from 43.7 ft.