A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of theexam, scores are normally distributed with =524. The teacher obtains a random sample of 2000 students, puts them through the reviewclass, and finds that the mean math score of the 2000 students is 531 with a standard deviation of 113. Complete parts(a) through(d) below.

Test the hypothesis at the =0.10 level of significance. Is a mean math score of 531 statistically significantly higher than 524? Conduct a hypothesis test using theP-value approach.

Find theP-value.

Is the sample mean statistically significantlyhigher?

yes or no

Test the hypothesis at the =0.10 level of significance with n=375 students. Assume that the sample mean is still 531 and the sample standard deviation is still 113. Is a sample mean of 531 significantly more than 524? Conduct a hypothesis test using theP-value approach.

Find the test statistic.

t0=

(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is

.

(Round to three decimal places asneeded.)