Rework Exercise 25, basing the decision on the P-value corresponding to the observed value of the test statistic.

Exercise 25

According to the norms established for a reading comprehension test, eighth graders should average 84.3 with a standard deviation of 8.6. If 45 randomly selected eighth graders from a certain school district averaged 87.8, use the four steps in the initial part of Section 1 to test the null hypothesis μ = 84.3 against the alternative μ > 84.3 at the 0.01 level of significance.

Q27;

The security department of a factory wants to know whether the true average time required by the night guard to walk his round is 30 minutes. If, in a random sample of 32 rounds, the night guard averaged 30.8 minutes with a standard deviation of 1.5 minutes, determine whether this is sufficient evidence to reject the null hypothesis μ = 30 minutes in favor of the alternative hypothesis μ  30 minutes. Use the four steps in the initial part of Section 1 and the 0.01 level of significance.