28. The school nurse of a certain high school claims that the mean age of Grade 11 students is 16 years old. The mean age of the randomly selected 35 Grade 11 students is 17 years old, which is different to what is claimed by the health worker. What will be the null hypothesis and the alternative hypothesis? A. \( H_{0}: \mu=16 \) and \( H_{1}: \mu \neq 16 \) B. \( H_{0}: \mu=16 \) and \( H_{1}: \mu<16 \) C. \( H_{0}: \mu=16 \) and \( H_{1}: \mu>16 \) D. \( H_{0}: \mu=16 \) and \( H_{a}: \mu \geq 16 \) 29. Mr. Arq, a Mathematics teacher, conducted a study on the impact of shifting to blended modality on the academic performance of his grade 9 students in Albay. In his survey, he found out that the mean score of one of his classes is 83 , with a standard deviation of 4 . The population mean score is 85 , with a standard deviation of 3 . Using a 0.10 level of significance to test the hypothesis, what is the value of \( \bar{x} \) in this problem? A. 3 B. 4 C. 83 D. 85 30. Which of the following pairs of hypotheses is correct? A. \( \mathrm{H}_{0} \) : The mean grade in Statistics of Grade 11 GAS is greater than 85. \( \mathrm{H}_{1} \) : The mean grade in Statistics of Grade 11 GAS is less than 85. B. \( \mathrm{H}_{0} \) : The proportion of SHS graduates who continue tertiary education is at least 0.40 . \( \mathrm{H}_{1} \) : The proportion of SHS graduates who continue tertiary education is less than 0.40 . C. \( \mathrm{H}_{0} \) : The average number of passengers that can be accommodated in a motor banca is 22. \( \mathrm{H}_{1} \) : The average number of passengers that can be accommodated in a motor banca is less than or equal to 22. D. \( \mathrm{H}_{0} \) : The proportion of SHS students under General Academic Strand is less than \( 35 \% \). \( \mathrm{H}_{1} \) : The proportion of students under General Academic Strand is \( 35 \% \) 31. Which test-statistic is appropriate to use when the population variance is known? A. Chi-Squared test B. F-test C. t-test D. z-test 32. What is the appropriate rejection region for a two-tailed test with a significant level of 0.05 and a sample size of 50 ? A. The rejection region is at \( \pm 1.96 \), and this means that when the computed test statistic is less than -1.96 or greater than 1.96 , the null hypothesis will be rejected. B. The rejection region is at \( \pm 1.96 \), and this means that when the computed test statistic is less than -1.96 or greater than 1.96 , the alternative hypothesis will be rejected. C. The rejection region is at \( \pm 2.58 \), and this means that when the computed test statistic is less than -2.58 or greater than 2.58 , the null hypothesis will be rejected. D. The rejection region is at \( \pm 2.58 \), and this means that when the computed test statistic is less than -2.58 or greater than 2.58 , the null hypothesis will be rejected.
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Question 17 A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of nine professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05? Group of answer choices No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so it is not supported. No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so it is not supported. Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so it is supported. Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so it is supported. Question 18 A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 28 residents in that town has a mean credit card debt of $3590 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set? Group of answer choices Yes, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is null, so it is supported. Yes, since p-value of 0.12 is less than 0.55, reject the null. Claim is alternative, so it is supported. No, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is alternative, so it is not supported. No, since p-value of 0.12 is greater than 0.10, reject the null. Claim is null, so it is not supported. Question 19 A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars from this company have an average gas mileage of 25.6 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set? Group of answer choices No, since the test statistic of -1.13 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so it is not supported. Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so it is supported. No, since the test statistic of -1.13 is close to the critical value of -1.24, the null is not rejected. The claim is the null, so it is supported. Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so it is supported. Question 20 A researcher wants to determine if extra homework problems help 8th grade students learn algebra. One 8th grade class has extra homework problems and another 8th grade class does not. After 2 weeks, both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups? Group of answer choices That the group without extra homework problems receives different instruction That each class has similar average IQs or abilities in mathematics That the group with the extra homework problems has fewer after school activities That each class of students has similar ages at the time of the testing
Thuc N.
Question 17: An environmentalist estimates that the mean waste recycled by adults in the United States is more than 1 pound per person per day. You want to test this claim with the burden of proof placed on the alternate hypothesis. You find that the mean waste recycled per person per day for a random sample of 12 adults in the US is 1.46 pounds with a standard deviation of 0.28 pounds. What is the result of this claim at an alpha level of .05. (remember Ho is u <= 1lb) a. Accept Ho since t calculated (-5.691) is less than critical t (1.796) b. Accept Ho since t calculated (5.691) is greater than critical t (-1.796) c. Reject Ho since t calculated (5.691) is greater than critical t (1.796) d. Reject Ho since t calculated (5.691) is greater than critical t (2.201) Question 18: An employment information service claims the mean annual pay for full-time female workers over age 25 and without a high school diploma is $19,100. The annual pay for a random sample of 12 full-time female workers without a high school diploma provided a mean of $18,886 and a standard deviation of $1,397. Test the claim at an alpha of .05 level that the pay for female workers without a high school diploma is equivalent to $19,100 per year. a. Accept the claim because t calculated of -0.531 is between critical t values of -2.201 and 2.201 b. Reject the claim because t calculated of -0.531 is greater than the critical t value of -2.201 c. Accept the claim because t calculated of -0.531 is less than a calculated t value of 1.796 d. Accept the claim because t calculated of -0.531 is between critical t values of -1.769 and 1.769 e. None of the above is true Question 19: The dean of a University estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample for a number of classroom hours for eight full-time faculty for one week provided a mean of 10.05 hours and a standard deviation of 2.485 hours. Test the claim that the number of faculty classroom hours per week is equal to 11 at an alpha level of .01. Choose the best possible answer. a. Accept the claim since t calculated of -1.081 is between the critical t values of -1.895 and 1.895 b. Accept the claim since t calculated of -1.081 is between the critical t values of -3.499 and 3.499 c. Reject the claim since t calculated of -1.081 is less than the critical t values of -0.896 d. Reject the claim since t calculated of -1.081 does not fall between the critical t values e. None of the above
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