Question

# From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n...

From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80. State your conclusion about H0 at significance level 0.01. Question 2 options: Test statistic: t = 1.61. P-value = 0.9356. Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is very strong. Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate. Test statistic: t = 1.61. P-value = 0.9463. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is weak or none. Test statistic: t = 1.61. P-value = 0.9356. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is weak or none.

Given:

= 80, n = 16, = 84.5, SD(S) = 11.2, = 0.01

Hypothesis:

Ho: = 80

Ha: < 80

Test statistic:

Degrees of Freedom = n- 1= 16-1 = 15

P-value = 0.0644 ...................Using t table

Conclusion:

P-value > , i.e. 0.0644 > 0.01, That is Fail to Reject Ho at 1% level of significance.

B.  Test statistic: t = 1.61. P-value = 0.0644. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is moderate.