- Question 3

The $p$-value for a hypothesis test turns out to be 0.07834 . At a $2 \%$ level of significance, what is the proper decision?
Reject $\mathrm{H}_{0}$
Fail to reject $H_{0}$
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Step 1 ：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 significance of the observed difference.

Step 2 ：In hypothesis testing, if the p-value is less than or equal to the level of significance (α), we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.

Step 3 ：In this case, the p-value is 0.07834 and the level of significance is 2% or 0.02. We need to compare these two values to make a decision.

Step 4 ：Since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

Step 5 ：Final Answer: The proper decision at a 2% level of significance is to \(\boxed{\text{Fail to reject } H_{0}}\).