Math / Data & Statistics

QuestionP-value $=0.0000$ (Round to three decimal places as needed.) What is the conclusion about the null hypothesis?
A. Fail to reject the null hypothesis because the $P$ -value is less than or equal to the significance level, $\alpha$ .
B. Reject the null hypothesis because the $P$ -value is greater than the significance level, $\alpha$ . C. Reject the null hypothesis because the $P$ -value is less than or equal to the significance level, $\alpha$ . D. Fail to reject the null hypothesis because the $P$ -value is greater than the significance level, $\alpha$ .

Studdy Solution

STEP 1

1. The P-value is given as $0.0000$ .
2. The significance level $\alpha$ is typically set at $0.05$ , $0.01$ , or $0.10$ unless otherwise specified.

STEP 2

1. Compare the P-value to the significance level $\alpha$ .
2. Determine the conclusion about the null hypothesis based on the comparison.

STEP 3

Assume a typical significance level, $\alpha = 0.05$ , unless specified otherwise.

STEP 4

Compare the P-value $0.0000$ to $\alpha = 0.05$ .
Since $0.0000 \leq 0.05$ , the P-value is less than or equal to the significance level.

STEP 5

Based on the comparison, determine the conclusion about the null hypothesis.
Since the P-value is less than or equal to $\alpha$ , we reject the null hypothesis.
The correct conclusion is:
C. Reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$ .

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