A math teacher claims that she has developed a review course that increases the

Question

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 =525. 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 530 with a standard deviation of 119. Complete parts (a) through (d) below.

(a) State the null and alternative hypotheses. Let mu be the mean score. Choose the correct answer below.

A. Upper H 0 : >525, H1 : 525H1: 525

B. Upper H 0 : mu equals 525H0: =525, Upper H 1 : mu not equals 525H1: 525

C. Upper H 0 : mu equals 525H0: =525, Upper H 1 : mu greater than 525H1: >525

D. Upper H 0 : mu less than 525H0: <525, Upper H 1 : mu greater than 525H1: >525

(b) Test the hypothesis at the alpha =0.10 level of significance. Is a mean math score of 530 statistically significantly higher than 525? Conduct a hypothesis test using the P-value approach. Find the test statistic. t = ___ (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?

Yes

No

(c) Do you think that a mean math score of 530 versus 525 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? No, because the score became only 0.95% greater. Yes, because every increase in score is practically significant.

(d) Test the hypothesis at thealphaequals=0.10level of significance withnequals=350350 students. Assume that the sample mean is still 530 and the sample standard deviation is still 119. Is a sample mean of 530 significantly more than 525?

Conduct a hypothesis test using the P-value approach.

Find the test statistic.

t = ___

(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?

Yes

No

What do you conclude about the impact of large samples on the P-value?

A. As n increases, the likelihood of not 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 rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.

Explanation / Answer

a)C. Upper H 0 : mu equals 525H0: =525, Upper H 1 : mu greater than 525H1: >525

b) for n=2000

std error =std deviation/(n)1/2=2.6609

hence test statt=(X-mean)/std error =1.879

p value for above =0.0301

Is the sample mean statistically significantly higher? Yes

D. As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.

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