Question

Amath 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 p=512. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 518 with a standard deviation of 110. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Let u be the mean score. Choose the correct answer below O A. Hop=512. H: 512 B. Hop=512. H,:> 512 OC. How >512, H, #512 OD. Hou <512, H, >512 (b) Test the hypothesis at the a=0.10 level of significance. Is a mean math score of 518 statistically significantly higher than 512? Conduct a hypothesis test using the P-value approach Find the test statistic to = 2.56 (Round to two decimal places as needed.) Find the P-value More

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Answer 1

INSTITUTE OF TANTS OF INO Suppose Xit the exam score , than - xu Nl M=512) Sample size=h=2200 Sample mean =X = 518 Sample std dev=8=110 we size x = 0 (a) The null hypothesis is that there is no significant difference after review course, in the scores of students i en e Ho: M=512 The alternative hypothesis is that there = is a significant increment in the sures of students after Inview course Hai M7512 The test statistic is 1 (6) 7 - X-M 8 h = 518 - 512 110/2200 = 2.5584

BERGHIEN Z= 2.56 Now p-value = P(Z >2:5584) - şsince it is a night tailed test? = - PZ < 2.5584) en = -0.9947 In excel - 0.0053 =NORM-S.DIST Tp-value = 0.005 3 (2.5584,1) P-value <x=0.10 hence we reject to and conclude that there is significant increment in the scores of students after review course Tues Sample mean statistically significantly - highes (c) yes, because every increase in score is practically significant (d) Je = 518, 8=110, n= 375 Z= 518-512 = 1.0563 110375 TZ=1.06

We use Z-test because sample size is large enough (1230) P-value = P(Z >1.06 ) = 1 -P(Z <1.06) 2 =NORM-S. DISTE = -0.8546 (1.0563, = 0.1454 Tp-value = 01145 up-value > x=0.10 hence we foul to reject Ho, so conclude that it there is no significant increment in scores efter review course. I No, Sample mean is not statistically significant higher. -p-value Impact of lange Option D is samples on correct. (4 Rnd RCL STO d/ SHIFT CALC SOLVE = 1 LA - 7 fabic Ir CASIO ENG IS-SUM ; fpS-VAR 1 PFDISTRZ D 0999 ALPHA d/dx : dx Ran 2 5 8 largi DEC ? EXP hyp's n c sin S-V.P.AM 3 6 9 COPY Labs Ans DRG ZO HEX 10 + x Pr DEL INS Con o cos? X! LO MODE