Question

A company produces electric devices operated by a thermostatic control. The standard deviation of the temperature where the controls operate should not exceed 2.0 degrees Fahrenheit. For a random sample of 20 of these controls, the sample standard deviation of operating temperatures was 2.36 degrees Fahrenheit.

i) Stating any necessary assumptions, test, at the 5% level, the null hypothesis that the population standard deviation is 2.0 against the alternative that it is larger.

ii) Create a 90% confidence interval for the population variance.

Answer 1

To Test :-

H0 :-  

H1 :-  

n = 20

Test Statistic :-

= ( ( 20-1 ) * 5.5696 ) / 4
= 26.4556

Test Criteria :-
Reject null hypothesis if

= 26.4556 < 30.144 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( > 26.4556 )
P value = 0.118
Reject null hypothesis if P value <
Since P value = 0.118 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence too support the claim that  the standard deviation of the temperature where the controls operate should not exceed 2.0 degrees Fahrenheit at 5% level of significance.

n = 20




Lower Limit =
Upper Limit =
90% Confidence interval is ( 3.5106 , 10.4599 )
( 3.5106 < < 10.4599 )