a) If sample data are such that the null hypothesis is rejected at the alpha=5% level...

a) If sample data are such that the null hypothesis is rejected at the alpha=5% level of significance based upon a 2 tailed test, is H0 also rejected at the alpha=1% level of significance ? Explain. b) If a 2 tailed hypothesis test leads to rejection of the null hypothesis at a certain level of significance, would the corresponding 1 tailed test lead to rejection of the null hypothesis ? Explain.

Solutions

Expert Solution

a) Let the test statistic be . Now for the 2 tailed test, the p-value is

Since , the null hypothesis is rejected at the alpha=5% level of significance , we have

It does not mean that , because the p-value can be . In that case the second condition is not satisfied.

That is H0 also rejected at the alpha=1% level of significance need to be TRUE.

b) Let the test statistic be . Now for the 2 tailed test, the p-value is

Since , the null hypothesis is rejected at the alpha=5% level of significance , we have

The p-value of the one tailed test is

is satisfied.

Thus, the corresponding 1 tailed test leads to rejection of the null hypothesis. (is TRUE).

milcah answered 11 months ago

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