Assume a significance level of \( \alpha=0.05 \) and use the given information to complete parts (a) and (b) below. Original claim: The mean pulse rate (in beats per minute) of a certain group of adult males is 76 bpm . The hypothesis test results in a P-value of 0.0697 . a. State a conclusion about the null hypothesis. (Reject \( \mathrm{H}_{0} \) or fail to reject \( \mathrm{H}_{0} \).) Choose the correct answer below. A. Reject \( \mathrm{H}_{0} \) because the P -value is greater than \( \alpha \). B. Reject \( \mathrm{H}_{0} \) because the P -value is less than or equal to \( \alpha \). C. Fail to reject \( H_{0} \) because the \( P \)-value is greater than \( \alpha \). D. Fail to reject \( H_{0} \) because the P -value is less than or equal to \( \alpha \).

C. Fail to reject \( H_{0} \) because the \( P \)-value is greater than \( \alpha \). When the P-value (0.0697) is greater than the significance level (\( \alpha = 0.05 \)), it indicates that there isn't enough evidence to reject the null hypothesis, which in this case is that the mean pulse rate of the adult males is 76 bpm. It’s like saying, "We're not convinced there's something unusual going on with their pulse rates!" In hypothesis testing, the choice of \( \alpha \) is crucial as it dictates how much risk you’re willing to take in making a Type I error, which is rejecting a true null hypothesis. When our P-value exceeds \( \alpha \), it suggests we should remain cautious. This means the evidence is not strong enough to shift our beliefs about the population mean pulse rate just yet!