Question

Which of the following statements about rejecting the null hypothesis is true? Group of answer choices If the p-value is such that you can reject Ho for a 5% level of significance, you can always reject it for a 1% level of significance. If the sample data is such that for a one-tailed test of the mean you can reject Ho at the 1% level of significance, you can always reject Ho for a two-tailed test at the same level of significance. If the p-value is such that you can reject H­o for a 1% level of significance, you can always reject it for a 5% level of significance. If the sample data is such that for a one-tailed test of the mean you can reject Ho at the 5% level of significance, you can always reject Ho for a two-tailed test at the 1% level of significance.

Answer 1

option A is incorrect because rejecting the null hypothesis at 5% level means that p value must be less than 0.05, but it does not mean that p value is less than 0.01. So, we can reject the Ho at 1% level just because the p value is less than 5%

option B is incorrect because p value for the two tailed hypothesis test is always twice of one tailed test p value, so it is possible that for two tailed hypothesis test the p value will be greater than 1%. So, statement is incorrect

option C is correct because when p value is less than 1%, then it is always less than 5%. So, we will definitely reject Ho at 5%, when Ho is rejected at 1% level.

option D is incorrect because rejecting the null hypothesis at 5% level means that p value must be less than 0.05, but it does not mean that p value is less than 0.01. So, we can reject the Ho at 1% level just because the p value is less than 5%