Question

a. If for the test of H0: μ = μ h   vs. Ha: μ ≠ μ h the null hypothesis cannot be rejected at α = .05, then it ______ be rejected at α = .10 for the test of H0: μ = μ h   vs. Ha: μ > μ h.

A. might B. must always C. will never

​​​​​​​b. If the 80% confidence interval for μ contains the value μ h, then the P-value for the test of H0: μ = μ h vs. Ha: μ ≠ μ h ______ be less than .20.

A. might B. must always C. will never

c. ​​​​​​​If for the test of H0: μ = μ h vs. Ha: μ ≠ μ h the null hypothesis cannot be rejected at α = .02, then the 98% confidence interval for μ   ______ contain the value μ h.

A. might B. must always C. will never

Answer 1

a. We reject Ho when the p Value is less than alpha . Here we fail to reject Ho at alpha= 0.05 . That means p value is more than 0.05

But we can't say that this Ho will not be rejected at alpha= 0.1 . because p Value may be more than 0.05 but less than 0.1 . In that case Ho will be rejected.

So correct option is , it Might be rejected at alpha= 0.10

b . 80% confidence Interval contains the value of Mu means we fail to Reject the null hypothesis. Confidence level 80% means alpha level is 20% or 0.2 . That means p value should be always more than 0.2 so that the null Hypothesis is not Rejected.

Correct option is , p value will never be less than 0.2

c. Null Hypothesis can't be rejected at alpha = 0.02 level or 2% level . That means the 98% confidence interval will always contain the value of Mu .

Correct option, must always contain the value of mu .