Question

3. Suppose the population mean is hypothesized to be 368 with a population standard deviation of 13. Sample data is obtained to test this hypothesis (n=36, the sample mean is 373).

a) Set up the two-tailed hypothesis test.

b) Test the hypothesis using the .01 level of significance. Also test at the .05 level of significance.

c) Interpret the results.

Answer 1

a)

H0: = 368

Ha: 368

b)

Critical value Z(α/2) = Z( 0.01 /2 ) = 2.576
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 373 - 368 ) / ( 13 / √( 36 ))
Z = 2.31

At 0.01 significance level,

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.01 /2 ) = 2.576
| Z | > Z( α/2 ) = 2.31 < 2.576
Result :- Fail to reject null hypothesis

At 0.05 significance level,

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 2.31 > 1.96
Result :- Reject null hypothesis

c)

For 0.01 significance level -

We conclude that we do not have sufficient evidence to support the claim.

For 0.05 significance level -

We conclude that we have sufficient evidence to support the claim.