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Suppose a new standardized test is given to 102 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 61 points, and the sample standard deviation, Sy, is 10 points. The authors plan to administer the test to all third-grade students in New Jersey. The 95% confidence interval for the mean score of all New Jersey third graders is (Round your responses to two decimal places.) Suppose the same test is given to 204 randomly selected third graders from Iowa, producing a sample average of 65 points and sample standard deviation of 13 points. The 90% confidence interval for the difference in mean scores between Iowa and New Jersey is (Round your responses to two decimal places.) (Round your response to four decimal places.) The p-value of the test of no difference in means versus some difference is Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are different. C. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are not different.

Suppose a new standardized test is given to 102 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 61 points, and the sample standard deviation, Sy, is 10 points. The authors plan to administer the test to all third-grade students in New Jersey. The 95% confidence interval for the mean score of all New Jersey third graders is (Round your responses to two decimal places.) Suppose the same test is given to 204 randomly selected third graders from Iowa, producing a sample average of 65 points and sample standard deviation of 13 points. The 90% confidence interval for the difference in mean scores between Iowa and New Jersey is (Round your responses to two decimal places.) (Round your response to four decimal places.) The p-value of the test of no difference in means versus some difference is Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are different. C. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are not different.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose a new standardized test is given to 102 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 61 points, and the sample standard deviation, Sy, is 10 points. The authors plan to administer the test to all third-grade students in New Jersey. The 95% confidence interval for the mean score of all New Jersey third graders is (Round your responses to two decimal places.) Suppose the same test is given to 204 randomly selected third graders from Iowa, producing a sample average of 65 points and sample standard deviation of 13 points. The 90% confidence interval for the difference in mean scores between Iowa and New Jersey is (Round your responses to two decimal places.) (Round your response to four decimal places.) The p-value of the test of no difference in means versus some difference is Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are different. C. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are not different.
Transcribed Image Text:Suppose a new standardized test is given to 102 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 61 points, and the sample standard deviation, Sy, is 10 points. The authors plan to administer the test to all third-grade students in New Jersey. The 95% confidence interval for the mean score of all New Jersey third graders is (Round your responses to two decimal places.) Suppose the same test is given to 204 randomly selected third graders from Iowa, producing a sample average of 65 points and sample standard deviation of 13 points. The 90% confidence interval for the difference in mean scores between Iowa and New Jersey is (Round your responses to two decimal places.) (Round your response to four decimal places.) The p-value of the test of no difference in means versus some difference is Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are different. C. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for lowa and New Jersey students are not different.
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