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uppose a new standardized test is given to 100 randomly selected third- rade students in New Jersey. The sample average score Y on the test is 8 points, and the sample standard deviation, sy, is 8 points. . The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders. . Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and sample stan- dard deviation of 11 points. Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. c. Can you conclude with a high degree of confidence that the popula- tion means for Iowa and New Jersey students are different? (What is the standard error of the difference in the two sample means? What is the p-value of the test of no difference in means versus some differ- ence?)

uppose a new standardized test is given to 100 randomly selected third- rade students in New Jersey. The sample average score Y on the test is 8 points, and the sample standard deviation, sy, is 8 points. . The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders. . Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and sample stan- dard deviation of 11 points. Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. c. Can you conclude with a high degree of confidence that the popula- tion means for Iowa and New Jersey students are different? (What is the standard error of the difference in the two sample means? What is the p-value of the test of no difference in means versus some differ- ence?)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Suppose a new standardized test is given to 100 randomly selected third- grade students in New Jersey. The sample average score Y on the test is 58 points, and the sample standard deviation, Sy, is 8 points. a. The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders. b. Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and sample stan- dard deviation of 11 points. Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. c. Can you conclude with a high degree of confidence that the popula- tion means for Iowa and New Jersey students are different? (What is the standard error of the difference in the two sample means? What is the p-value of the test of no difference in means versus some differ- ence?)
Transcribed Image Text:Suppose a new standardized test is given to 100 randomly selected third- grade students in New Jersey. The sample average score Y on the test is 58 points, and the sample standard deviation, Sy, is 8 points. a. The authors plan to administer the test to all third-grade students in New Jersey. Construct a 95% confidence interval for the mean score of all New Jersey third graders. b. Suppose the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and sample stan- dard deviation of 11 points. Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. c. Can you conclude with a high degree of confidence that the popula- tion means for Iowa and New Jersey students are different? (What is the standard error of the difference in the two sample means? What is the p-value of the test of no difference in means versus some differ- ence?)
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