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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 u = 519. 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 525 with a standard deviation of 110. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Họ: = 519, H > 519 (b) Test the hypothesis at the a= 0.10 level of significance. Is a mean math score of 525 statistically significantly higher than 519? Conduct a hypothesis test using the P-value approach. Find the test statistic. h= 2.31 (Round to two decimal places as needed.) Find the P-value The P-value is 0.010. (Round to three decimal places as needed.) Is the sample mean statistically significantly higher? A. No, because the P-value is less than a= 0.10. B. No, because the P-value is greater than a= 0.10. C. Yes, because the P-value greater than a = 0.10 D. Yes, because the P-value less than a=0.10. (c) Do you think that a mean math score of 525 versus 519 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? A. Yes, because every increase in score is practically significant. B. Yes, because the score became more than 1.16% greater. C. No, because every increase in score is practically significant. D. No, because the score became only 1.16% greater.

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 u = 519. 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 525 with a standard deviation of 110. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Họ: = 519, H > 519 (b) Test the hypothesis at the a= 0.10 level of significance. Is a mean math score of 525 statistically significantly higher than 519? Conduct a hypothesis test using the P-value approach. Find the test statistic. h= 2.31 (Round to two decimal places as needed.) Find the P-value The P-value is 0.010. (Round to three decimal places as needed.) Is the sample mean statistically significantly higher? A. No, because the P-value is less than a= 0.10. B. No, because the P-value is greater than a= 0.10. C. Yes, because the P-value greater than a = 0.10 D. Yes, because the P-value less than a=0.10. (c) Do you think that a mean math score of 525 versus 519 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance? A. Yes, because every increase in score is practically significant. B. Yes, because the score became more than 1.16% greater. C. No, because every increase in score is practically significant. D. No, because the score became only 1.16% greater.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Educational Content on Hypothesis Testing 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 a mean (\(\mu\)) of 519. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of these students is 525 with a standard deviation of 110. We will conduct a hypothesis test to evaluate this claim. #### (a) State the Null and Alternative Hypotheses - Null hypothesis (\(H_0\)): \(\mu = 519\) - Alternative hypothesis (\(H_1\)): \(\mu > 519\) #### (b) Test the Hypothesis at the \(\alpha = 0.10\) Level of Significance **Objective:** Determine if a mean math score of 525 is statistically significantly higher than 519 using the P-value approach. 1. **Calculate the Test Statistic:** - Test statistic: \(t_0 = 2.31\) - (Rounded to two decimal places as needed.) 2. **Find the P-value:** - P-value = 0.010 - (Rounded to three decimal places as needed.) 3. **Decision:** Is the sample mean statistically significantly higher? - **Answer D:** Yes, because the P-value is less than \(\alpha = 0.10\). #### (c) Practical Significance of the Result Assess if a mean math score of 525 versus 519 will affect decisions made by school admissions administrators. Does this increase in score have any practical significance? - **Selection C:** No, because every increase in score is practically significant. However, this box is likely erroneously marked. The options (d) seem more appropriate given typical considerations of practical significance. Explore further to determine the practical impact, as the options suggest varying interpretations: - **Option A:** Increase is practically significant. - **Option B:** Increase is more than 1.16% greater. - **Option D:** Score increase is only 1.16% greater. Understanding both statistical and practical significance is crucial in effectively applying hypothesis testing to real-world decisions.
Transcribed Image Text:### Educational Content on Hypothesis Testing 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 a mean (\(\mu\)) of 519. The teacher obtains a random sample of 1800 students, puts them through the review class, and finds that the mean math score of these students is 525 with a standard deviation of 110. We will conduct a hypothesis test to evaluate this claim. #### (a) State the Null and Alternative Hypotheses - Null hypothesis (\(H_0\)): \(\mu = 519\) - Alternative hypothesis (\(H_1\)): \(\mu > 519\) #### (b) Test the Hypothesis at the \(\alpha = 0.10\) Level of Significance **Objective:** Determine if a mean math score of 525 is statistically significantly higher than 519 using the P-value approach. 1. **Calculate the Test Statistic:** - Test statistic: \(t_0 = 2.31\) - (Rounded to two decimal places as needed.) 2. **Find the P-value:** - P-value = 0.010 - (Rounded to three decimal places as needed.) 3. **Decision:** Is the sample mean statistically significantly higher? - **Answer D:** Yes, because the P-value is less than \(\alpha = 0.10\). #### (c) Practical Significance of the Result Assess if a mean math score of 525 versus 519 will affect decisions made by school admissions administrators. Does this increase in score have any practical significance? - **Selection C:** No, because every increase in score is practically significant. However, this box is likely erroneously marked. The options (d) seem more appropriate given typical considerations of practical significance. Explore further to determine the practical impact, as the options suggest varying interpretations: - **Option A:** Increase is practically significant. - **Option B:** Increase is more than 1.16% greater. - **Option D:** Score increase is only 1.16% greater. Understanding both statistical and practical significance is crucial in effectively applying hypothesis testing to real-world decisions.
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