Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. A test of sobriety involves measuring the subject's motor skills. A study of n = 20 randomly selected sober subjects take the test and produce a mean score of X = 41.0, and we know that o = 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is more than 35.0. (Hint: Hypothesis Test for 1 Mean, sigma known) O Ho: u = 41; H1: < 41. Test statistic: z = -7.25. P-value: 0.9999. Because the P-value is greater than the significance level of 0.01, 2 we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the true mean score for all sober subjects is more than 35. Ho: u = 35; H1:> 25. Test statistic: z = 7.25. P-value: 0.0001. Because the P-value is less than the significance level of 0.01, 2 we reject the null hypothesis. There is sufficient evidence to support the claim that the true mean score for all sober subjects is more than 35,

Answer 1

Correct option:

H0; $\mu$ = 35, H1: $\mu$ > 35, Test Statistic: Z = 7.25. P - value = 0.0001. Bcause the P - value is less than the significance level of 0.01, we reject the null hypothesis. There is sufficient evidence to support the claim that the true mean score for all sober subjcts is more than 35

Explanation:

H0; $\mu$ = 35, (the true mean score for all sober subjcts is not more than 35)

H1: $\mu$ > 35, (the true mean score for all sober subjcts is more than 35) (Claim)

Test Statistic is given by:

T-HO Z 41 – 35 3.7/20 = 7.25 o/vñ

By Technology:

P- Value =0.0001

Since P- Value =0.0001 isless than $\alpha$ = 0.01, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the true mean score for all sober subjcts is more than 35.