Questions: The P-value for a hypothesis test is shown. Use the P-value to decide whether or not to reject the null hypothesis. P=0.0461

Solution Steps

To decide whether to reject the null hypothesis using the P-value, we need to compare the P-value to a significance level (commonly denoted as \(\alpha\)). A typical significance level is 0.05. If the P-value is less than or equal to \(\alpha\), we reject the null hypothesis; otherwise, we do not reject it.

We are given the P-value for a hypothesis test: \[ P = 0.0461 \] We also have a common significance level: \[ \alpha = 0.05 \]

To decide whether to reject the null hypothesis, we compare the P-value to the significance level \(\alpha\): \[ P \leq \alpha \]

Since \(P = 0.0461\) and \(\alpha = 0.05\), we compare the two values: \[ 0.0461 \leq 0.05 \] This inequality is true.

Final Answer