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 mu = 523. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of the 1800 students is 529 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. H_0: mu > 523, H_1: mu notequalto 523 B. H_0: mu = 523, H_1:mu notequalto 523 C. H_0: mu 523 D. H_0: mu = 523, H_1: mu > 523 (b) Test the hypothesis at the alpha = 0.10 level of significance, is a mean math score of 529 statistically significantly higher than 523? Conduct a hypothesis test using the P-value approach. Find the test statistic. t_0 = (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 529 versus 523 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 1.15% greater. (d) Test the hypothesis at the alpha = 0.10 level of significance with n = 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 523? Conduct a hypothesis test using the P-value approach. Find the test statistic. t_0 = (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 statistical significantly higher? No Yes What do you conclude about the impact or 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 insignificant differences. B. As n increases, the likelihood of not 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 n hypothesis increases. However, large samples tend to overemphasize practically significant differences.

Explanation / Answer

Part a)

Answer: D. Ho: µ = 523, H1: µ > 523

Part b)

t = (x bar – Mew)/ (s/sqrt(n))

   = (529-523)/(119/sqrt (1800))

   = 2.14

Answer : to = 2.14

P-value: we use excel to get the p-value

=TDIST (2.14, 1799,1)

= 0.016

Answer: The P value is 0.016

P-value is less than 0.10 so we reject the null hypothesis.

Is the sample mean statistically significantly higher?

Answer: Yes

Part c)

Answer: Yes, because every increase in score is practically significant.

Part d)

t = (x bar – Mew)/ (s/sqrt(n))

   = (529-523)/(119/sqrt (375))

   = 0.98

Answer: to = 0.98

P-value: =TDIST(0.98,374,1)

Answer: The P-value is 0.164

P-value is more than 0.10; we fail to reject the null hypothesis.

Answer: No

Answer: D. As n increases the likelihood of rejecting the null hypothesis increases. However large samples tend to overemphasize practically significant differences.

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