Question

# A math teacher claims that she has developed a review course that increases the scores of...

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 mu equals515. 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 520 with a standard deviation of 117. 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 : mu greater than 515​, Upper H 1 : mu not equals 515 B. Upper H 0 : mu equals 515​, Upper H 1 : mu not equals 515 C. Upper H 0 : mu equals 515​, Upper H 1 : mu greater than 515 D. Upper H 0 : mu less than 515​, Upper H 1 : mu greater than 515 ​(b) Test the hypothesis at the alpha equals0.10 level of significance. Is a mean math score of 520 statistically significantly higher than 515​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Find the​ P-value. The​ P-value is nothing. ​(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 520 versus 515 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 0.97​% greater. ​Yes, because every increase in score is practically significant. ​(d) Test the hypothesis at the alphaequals0.10 level of significance with nequals400 students. Assume that the sample mean is still 520 and the sample standard deviation is still 117. Is a sample mean of 520 significantly more than 515​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) Find the​ P-value. The​ P-value is nothing. ​(Round to three decimal places as​ needed.) Is the sample mean statistically significantly​ higher? No Yes 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 significant 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 insignificant differences. D. As n​ increases, the likelihood of rejecting the null hypothesis increases.​ However, large samples tend to overemphasize practically insignificant differences. Click to select your answer(s).

Ans:

a)

H 0 : mu equals 515​,

H 1 : mu greater than 515

b)alpha=0.1

critical z value=1.282

Test statistic:

t=(520-515)/(117/SQRT(2000))

t=1.91

p-value=0.028

Reject the null hypothesis,as p-value<0.1

Yes

c)yes, because every increase in score is practically significant.

d)

t=(520-515)/(117/SQRT(400))

t=0.85

p-value=0.197

No,not significant.

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