Question

er 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=517517. The teacher obtains a random sample of 20002000 ​students, puts them through the review​ class, and finds that the mean math score of the 20002000 students is 523523 with a standard deviation of 110110. 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 less than 517H0: μ<517​, Upper H 1 : mu greater than 517H1: μ>517 B. Upper H 0 : mu equals 517H0: μ=517​, Upper H 1 : mu greater than 517H1: μ>517 Your answer is correct.C. Upper H 0 : mu greater than 517H0: μ>517​, Upper H 1 : mu not equals 517H1: μ≠517 D. Upper H 0 : mu equals 517H0: μ=517​, Upper H 1 : mu not equals 517H1: μ≠517 ​(b) Test the hypothesis at the alpha equalsα=0.100.10 level of significance. Is a mean math score of 523523 statistically significantly higher than 517517​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0t0equals=2.442.44 ​(Round to two decimal places as​ needed.) Find the​ P-value. The​ P-value is . 006.006. ​(Round to three decimal places as​ needed.) Is the sample mean statistically significantly​ higher? NoNo Your answer is not correct. YesYes This is the correct answer. ​(c) Do you think that a mean math score of 523523 versus 517517 will affect the decision of a school admissions​ administrator? In other​ words, does the increase in the score have any practical​ significance? ​Yes, because every increase in score is practically significant. ​No, because the score became only 1.161.16​% greater. Your answer is correct. ​(d) Test the hypothesis at the alphaαequals=0.10 level of significance with nequals=350350 students. Assume that the sample mean is still 523523 and the sample standard deviation is still 110110. Is a sample mean of 523523 significantly more than 517517​? Conduct a hypothesis test using the​ P-value approach. Find the test statistic. t 0t0equals=nothing ​(Round to two decimal places as​ needed.)

Answer 1

d)

n = 350