Question

This Question: 1 pt This Quiz: 17 pts possible Use a e-test to test the daim σ < 43 at the α-Ο.05 significance level using sample statistics s = 40.4 and n-12. Assume the population is normally distributed Identify the null and alternative hypotheses. На:0243 H:43 Ha : σ s 43 Identify the test statistic. (Round to three decimal places as needed.) Identify the critical value(s). Round to three Choose the correct conclusion below. 。A. Fail to reject Ho. There is not enough evidence at the 5% level of significance to support the claim. Reject Ho. There is not enough evidence at the 5% level of significance to support the claim B. O c. Fail to reject Ho. There is enough evidence at the 5% level of significance to support the claim. Reject Ho. There is enough evidence at the 5% level of significance to support the claim. O D.

Answer 1

Hypothesis :

Но : σ > 43

( Claim )

Ho : σ < 43

Left tailed test.

Test statistic :

(n - 1)s2 2 = 2

Where , $\sigma$ is hypothesized population standard deviation = 43

s is sample standard deviation = 40.4

n is sample size = 12

So test statistic is ,

2 (12 - 1)40.42 432

29.710

Critical value :

Significance level =

a-0.05

Degrees of freedom ( df ) = n - 1 = 12- 1 =11

Critical value for this left tailed test is ,

           { Using Excel ,   =CHIINV(0.95,11) = 4.575 }

Xi-adf- χ0.95, 1,-4.575

Rejection Region : { $\chi ^2$ : $\chi ^2$ < 4.575 }

Decision about null hypothesis :

It is observed that test statistic ( 9.71 ) is greater than critical value ( 4.575 ).

So fail to reject null hypothesis H₀ .

Conclusion :

Fail to reject H₀. There is not enough evidence at the 5% level of significance to support the claim.