Questions: Reject or Not State whether or not the null hypothesis should be rejected on the basis of the given P-value. Part 1 of 2 (a) P-value = 0.2820, α=0.1, one-tailed test Reject the null hypothesis Do not reject the null hypothesis Part 2 of 2 (b) P-value = 0.2820, α=0.1, two-tailed test Reject the null hypothesis Do not reject the null hypothesis

Solution Steps

We are given two scenarios involving a $P$-value and a significance level $\alpha$. We need to determine whether to reject or not reject the null hypothesis based on the given $P$-value and the type of test (one-tailed or two-tailed).

• $P$-value: $0.2820$
• $\alpha$: $0.1$
• Test type: One-tailed test

In a one-tailed test, we compare the $P$-value directly to $\alpha$. If the $P$-value is less than or equal to $\alpha$, we reject the null hypothesis. Otherwise, we do not reject it.

Here, $0.2820 > 0.1$, so we do not reject the null hypothesis.

• $P$-value: $0.2820$
• $\alpha$: $0.1$
• Test type: Two-tailed test

In a two-tailed test, we compare the $P$-value to $\alpha/2$. If the $P$-value is less than or equal to $\alpha/2$, we reject the null hypothesis. Otherwise, we do not reject it.

Here, $\alpha/2 = 0.05$, and $0.2820 > 0.05$, so we do not reject the null hypothesis.

Final Answer