Assume a significance level of $\alpha=0.05$ and use the given information to complete parts (a) and (b) below.
Original claim: Less than $51 \%$ of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.1877 .
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 less than or equal to $\alpha$
B. Reject $\mathrm{H}_{0}$ because the P-value is greater than $\alpha$.
C. Fail to reject $\mathrm{H}_{0}$ because the $\mathrm{P}$-value is less than or equal to $\alpha$
D. Fali to reject $\mathrm{H}_{0}$ because the $\mathrm{P}$-value is greater than $\alpha$.
b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?
Answer
Since the P-value (0.1877) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, the correct answer is D. Fail to reject H0 because the P-value is greater than α. \(\boxed{D}\)
Step 1 ：The null hypothesis is that 51% or more of adults would erase all of their personal information online if they could. The alternative hypothesis is that less than 51% of adults would erase all of their personal information online if they could.
Step 2 ：The P-value is a measure of the probability that an observed difference could have occurred just by random chance. The lower the P-value, the greater the statistical evidence you have to reject the null hypothesis.
Step 3 ：The significance level (α) is a threshold set by the researcher to determine when a P-value is low enough to reject the null hypothesis. If the P-value is less than or equal to α, we reject the null hypothesis. If the P-value is greater than α, we fail to reject the null hypothesis.
Step 4 ：In this case, the P-value is 0.1877 and the significance level is 0.05. We need to compare these two values to determine whether to reject or fail to reject the null hypothesis.
Step 5 ：Since the P-value (0.1877) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, the correct answer is D. Fail to reject H0 because the P-value is greater than α. \(\boxed{D}\)
