Question

The significance level and p-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected.

2. α=0.01, p-value=0.12
a) Reject the null hypothesis
b) Fail to reject the null hypothesis

3. α=0.05, p-value=0.015
a) Reject the null hypothesis
b) Fail to reject the null hypothesis
1) Reject the null hypothesis
2) Fail to reject the null hypothesis

Answer 1

In hypothesis testing, comparing the p-value with the significance level determines whether to reject or not reject the null hypothesis. For a significance level of 0.01 and a p-value of 0.12, we fail to reject the null hypothesis. If the significance level is 0.05 and the p-value is 0.015, the null hypothesis is rejected.

Step-by-step explanation:

The question involves making a decision to reject or fail to reject the null hypothesis based on the provided significance level (alpha, α) and the p-value. To compare we shall follow the rule that if the p-value is less than the significance level, we reject the null hypothesis. Conversely, if the p-value is greater than the significance level, we fail to reject the null hypothesis.

With α=0.01 and a p-value=0.12, since the p-value is greater than the significance level (0.12 > 0.01), the decision is to fail to reject the null hypothesis.

For α=0.05 and a p-value=0.015, because the p-value is less than the significance level (0.015 < 0.05), we reject the null hypothesis.

The process to determine these decisions includes a systematic comparison between the alpha value and the observed p-value. This is a fundamental concept in hypothesis testing, relevant to the assessment of statistical evidence against a presumed null hypothesis.