TRUE/FALSE: Hypothesis Testing (Part 3/3) Please answer ‘True in all cases’ or ‘

Question

TRUE/FALSE: Hypothesis Testing (Part 3/3)

Please answer ‘True in all cases’ or ‘False for at least one case’. Briefly justify your answers.

(i) If a null hypothesis is rejected at a significance level of .05, it will always be rejected at a significance level of .01

(j) If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will always be rejected at the same significance level.

(k) Let X1, ..., Xn ~ N(µ, 2 ) (n large), H0: µ = µ0, H1: µ µ0 and suppose you conduct a hypothesis test and you fail to reject the null hypothesis. If you calculate the corresponding confidence interval, µ0 will be the center of the interval.

Explanation / Answer

1) the answer is false.

Reason:if null Hypothesis is rejected at significance level 0.05. it "sometimes rejected ata singnicancd level of 0.01.

2) the answer is "false "

Reason: If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will "sometimes rejected at the same significance level."

3)

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