Which of the following statements are true?
(A) In a two-tail test of hypothesis for a population mean the decision rule is to reject H0 if the test statistic lies outside of the action limits.
(B) A statistical test of hypothesis is performed under the assumption that the null hypothesis is false.
(C) A test of hypothesis for a population mean is called a lower tail test if the decision rule is to conclude H1 if the test statistic is less than the action limit.
(D) In the test of hypothesis for the claim that the mean grade of students in a statistics course is more than 70%, the type I error would consist of concluding that the mean is 70% or less when in fact it is greater than 70%.
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B and D
To determine which statements are true, let's analyze each statement:
(A) In a two-tail test of hypothesis for a population mean, the decision rule is to reject H0 if the test statistic lies outside of the action limits.
This statement is not true. In a two-tail test, the decision rule is to reject the null hypothesis (H0) if the test statistic lies outside of the critical region or falls in the rejection region.
(B) A statistical test of hypothesis is performed under the assumption that the null hypothesis is false.
This statement is true. In hypothesis testing, we assume the null hypothesis (H0) is true, and we gather evidence to determine if there is enough evidence to reject it in favor of the alternative hypothesis (H1).
(C) A test of hypothesis for a population mean is called a lower tail test if the decision rule is to conclude H1 if the test statistic is less than the action limit.
This statement is true. In a lower tail test, the decision rule is to reject the null hypothesis (H0) in favor of the alternative hypothesis (H1) when the test statistic falls below the critical value or action limit.
(D) In the test of hypothesis for the claim that the mean grade of students in a statistics course is more than 70%, the type I error would consist of concluding that the mean is 70% or less when, in fact, it is greater than 70%.
This statement is true. In hypothesis testing, a Type I error occurs when we reject the null hypothesis (H0) when it is actually true. In this case, the null hypothesis is that the mean grade is 70% or less, and a Type I error would be to incorrectly conclude that the mean grade is 70% or less when it is actually greater than 70%.
So, the true statements are: (B) and (D).