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 the exam, scores are normally distributed with μ = 516. The teacher obtains a random sample of 2000 students, puts them through the review class, and finds that the mean math score of the 2000 students is 521 with a standard deviation of 113. Complete parts (a) through (d) below.
(a) State the null and alternative hypotheses. Let μ be the mean score. Choose the correct answer below.
A. H0: μ = 516, H1: μ > 516
B. H0: μ < 516, H1: μ > 516
C. H0: μ > 516, H1: μ ≠ 516
D. H0: μ = 516, H1: μ ≠ 516
(b) Test the hypothesis at the α = 0.10 level of significance. Is a mean math score of 521 statistically significantly higher than 516? Conduct a hypothesis test using the P-value approach.
Find the test statistic.
t0 =
(Round to two decimal places as needed.)
Find the P-value.
The P-value is
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
a. Yes
b. No
(c) Do you think that a mean math score of 521 versus 516 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?
a. No, because the score became only 0.97% greater.
b. Yes, because every increase in score is practically significant.
(d) Test the hypothesis at the α = 0.10 level of significance with n = 375 students. Assume that the sample mean is still 521 and the sample standard deviation is still 113. Is a sample mean of 521 significantly more than 516? Conduct a hypothesis test using the P-value approach.
Find the test statistic.
t0 =
(Round to two decimal places as needed.)
Find the P-value.
The P-value is
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
a. Yes
b. No
What do you conclude about the impact of large samples on the P-value?
A. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.
B. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
C. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
D. As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.