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 mu equalsμ=524. 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 529 with a standard deviation of 119.

Complete parts​ (a) through​ (d) below.

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

A.Upper H 0 : mu greater than 524H0: μ>524​,

Upper H 1 : mu not equals 524H1: μ≠524

B.Upper H 0 : mu equals 524H0: μ=524​,

Upper H 1 : mu greater than 524H1: μ>524

C.Upper H 0 : mu less than 524H0: μ<524​,

Upper H 1 : mu greater than 524H1: μ>524

D.Upper H 0 : mu equals 524H0: μ=524​,

Upper H 1 : mu not equals 524

​(b) Test the hypothesis at the alpha equalsα=0.10 level of significance. Is a mean math score of 529 statistically significantly higher than 524​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic.

Find the​ P-value.

Is the sample mean statistically significantly​ higher?

​(c) Do you think that a mean math score of 529 versus 524 will affect the decision of a school admissions​ administrator? In other​ words, does the increase in the score have any practical​ significance?

(d) Test the hypothesis at the alphaαequals=0.10 level of significance with nequals=375 students. Assume that the sample mean is still 529 and the sample standard deviation is still 119.Is a sample mean of 529 significantly more than 524​? Conduct a hypothesis test using the​ P-value approach.

Find the test statistic.

Find the​ P-value.

Is the sample mean statistically significantly​ higher?

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 significant differences.

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

Answer 1