2. The prevalence rate of Hypertension among US adults is 30%. We plan to draw a random sample of 70 people from that population. What is the standard error of the sample proportion of hypertension? 0.003 0.055 0.065 0.210 3. We selected a random sample of size 120 from a pool of university students and asked whether they use Facebook on a regular basis. Sixty replied yes. What would be your estimation of the standard error of the sample proportion of regular Facebook users based upon the given information? 0.046 0.065 0.070 0.250 4. To investigate the prevalence rate of Hypertension among US adults, we drew a random sample of 65 adults from the US and among them 12 people had hypertension. Please construct a 95% confidence interval for the population proportion of hypertension. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical zvalue). [3.0%, 33.9%] [5.0%, 31.9%] [7.0%, 29.9%] [9.0%, 27.9%] 5. A random sample of size 120 was selected from a pool of university students and they were asked whether they use Facebook on a regular basis. Sixty replied yes. What would be your 90% confidence interval estimate of the population proportion of regular Facebook users based upon the given information? (Hint: use 1.65 as the critical zvalue) [42.5%, 57.5%] [44.5%, 55.5%] [46.5%, 53.5%] [48.5%, 51.5%] 6. Which of the following statements are correct regarding confidence intervals and sample size? Greater confidence requires narrower Confidence Interval. Smaller sample size gives narrower Confidence Interval. Larger sample size gives narrower Confidence Interval. Sample size has no impact on the size of Confidence Intervals. 7. It is known that the population standard deviation of the IQ test results is 16. Assuming that we have a random sample of 135, what is the standard error of the average IQ of a sample of this size? 1.38 1.83 2.71 3.16 8. Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample standard deviation is 10.6 mmHg. What is the estimated standard error of the sample mean? 0.05 0.75 1.50 3.00 9. It is known that the population standard deviation of the IQ test results is 16. Assuming that we have a random sample of 144 and a sample mean of 98, what would be your 90% confidence interval estimate of the population mean? (Hint: use 1.65 as the critical zvalue) [89.8, 106.2] [91.8, 104.2] [93.8, 102.2] [95.8, 100.2] 10. Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample mean is 115.0 mmHg and the sample standard deviation is 10.4 mmHg. Please construct a 95% confidence interval for the population mean of students' systolic blood pressure. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical zvalue) [107.6, 122.4] [109.6, 120.4] [111.6, 118.4] [113.6, 116.4] 11. To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement? The sample size is 36 and the population proportion under null hypothesis is 25%. The sample size is 48 and the population proportion under null hypothesis is 80%. The sample size is 99 and the population proportion under null hypothesis is 90%. The sample size is 200 and the population proportion under null hypothesis is 6%. 12. In One Sample Proportion test, it is critical to understand the direction of the alternative hypothesis. What are the directions of the following two examples of alternative hypotheses? 1) Ha: P < 0.3 2) Ha: P < 0.5 1) is left tailed and 2) is right tailed. 1) is right tailed and 2) is left tailed. Both are left-tailed Both are right-tailed 13. In One Sample Proportion test, it is important to convert the sample proportion to a zscore first. In this example, we selected a random sample of size 100 from a pool of university students and asked whether they use Facebook on a regular base. Seventy replied yes. Assuming that the population proportion under the null hypothesis is 50%, what is the zscore for the sample proportion? 1.00 2.00 3.00 4.00 14. To investigate the prevalence rate of Hypertension of a certain population, we drew a random sample of 70 people from that population and among them 8 people had hypertension. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Depending on the direction of the alternative test, use 1.65 or 1.65 as the critical zvalue) Ho: P = 0.2 (Null) Ha: P < 0.2 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 15. A random sample of size 120 was selected from a pool of university students and they were asked whether they use Facebook on a regular base. Fifty replied yes. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Depending on the direction of the alternative test, use 1.65 or 1.65 as the critical zvalue) Ho: P = 0.3 (Null) Ha: P > 0.3 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 16. A group of researchers from a medical firm are trying to understand the proportion of American adults who are allergic to a medication. In a random sample of 120 adults, 15 people say they have such an allergy. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Use 1.96 and 1.96 as the critical zvalues) Ho: P = 0.10 (Null) Ha: P 0.10 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 17. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred seventy three patients were recruited to participate in the clinical trial. In clinical testing, 60 out of 175 people taking the medication reported symptoms of anxiety. Of the other 198 people receiving a placebo, 80 reported symptoms of anxiety. Combining the two samples together, what is the overall proportion of those who reported symptoms of anxiety among all participants? 0.18 0.28 0.38 0.48 18. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred eighty patients were recruited to participate in the clinical trial. In clinical testing, 53 out of 200 people taking the medication reported symptoms of anxiety. Of the other 180 people receiving a placebo, 86 reported symptoms of anxiety. What is the estimated standard error of the difference of the two sample proportions based on pooled sample proportion? 0.039 0.049 0.059 0.069 19. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred eighty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. In clinical testing, 50 out of 180 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 70 reported symptoms of anxiety. Do you think if the patients in the two groups performed significantly different with respect to symptoms of anxiety? Please use 0.05 as the level of significance. (Hint: use 1.96 and 1.96 as the critical zvalues). Yes, the proportions were significantly different. No, the proportions were not significantly different. We don't have sufficient information to conduct the test. The data do not meet the independence requirement so we cannot use a z-test. 20. Researchers want to test the effectiveness of a new antianxiety medication. Four hundred twenty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. In clinical testing, 70 out of 220 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 105 reported symptoms of anxiety. If we use P1 to denote the population proportion of those who receive the medication and P2 of those who receive placebo, what would be your 95% Confidence Interval estimate for P1P2 based on the given information? Please note that to estimate the standard error of the difference of the sample proportions, you will use the two individual sample proportions instead of the pooled sample proportion. (Hint: Use 1.96 as your critical zvalue) [-0.299, -0.114] [-0.309, -0.104] [-0.319, -0.094] [-0.329, -0.084] 21. Thirteen undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 122.9 mmHg and 10.4 mmHg respectively. What is the obtained tscore for this sample under the null hypothesis Ho: = 120? -1.50 -1.01 1.01 1.50 22. Fourteen undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 125.8 mmHg and 10.8 mmHg respectively. What would be the rejection region if you were asked to test hypotheses Ho: = 120 versus Ha: > 120 with level of significance of 0.05? Please use the attached tdistribution table to find the critical t value. t > 1.782 t > 1.771 t > 1.761 t > 2.160 23. To compare the treatment effects of two medications, two independent samples of patient performance data were collected. The sample sizes are 10 and 12 respectively. Assuming that the two populations shared the same variance, the researchers decided to conduct a two independent samples test for the means. What would be the number of degrees of freedom for the obtained t statistic with these sample sizes? 20 21 22 23 24. To compare the treatment effect of two medications, two independent samples of patient performance data were collected. The sample sizes are 10 and 12 respectively. Assuming that the two populations shared the same variance, the researchers decided to conduct a two independent samples test for the means. They found that the difference between the two sample means was 3.0 and the pooled sample standard deviation of the two samples was 3.9. What would be the obtained tvalue under the null hypothesis that assumes no difference between the two population means? 1.08 1.80 2.08 2.41 25. A random sample of 120 fifth grade students took a standardized reading test and 100 of them (83.3%) met the minimum requirement of reading proficiency for the grade level. Among these students, sixty were males and among them 45 met the requirement (75%). Among the 60 female students, fifty five met the requirement (91.7%). Their English teacher is interested to see if there is significantly difference between boys and girls regarding the proportions of passing the test. Which of the following tests would you recommend? One-sample test for proportions Two-sample test for proportions One-sample test for means Two-sample test for means 2. The prevalence rate of Hypertension among US adults is 30%. We plan to draw a random sample of 70 people from that population. What is the standard error of the sample proportion of hypertension? 0.003 0.055 0.065 0.210 3. We selected a random sample of size 120 from a pool of university students and asked whether they use Facebook on a regular basis. Sixty replied yes. What would be your estimation of the standard error of the sample proportion of regular Facebook users based upon the given information? 0.046 0.065 0.070 0.250 4. To investigate the prevalence rate of Hypertension among US adults, we drew a random sample of 65 adults from the US and among them 12 people had hypertension. Please construct a 95% confidence interval for the population proportion of hypertension. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical zvalue). [3.0%, 33.9%] [5.0%, 31.9%] [7.0%, 29.9%] [9.0%, 27.9%] 5. A random sample of size 120 was selected from a pool of university students and they were asked whether they use Facebook on a regular basis. Sixty replied yes. What would be your 90% confidence interval estimate of the population proportion of regular Facebook users based upon the given information? (Hint: use 1.65 as the critical zvalue) [42.5%, 57.5%] [44.5%, 55.5%] [46.5%, 53.5%] [48.5%, 51.5%] 6. Which of the following statements are correct regarding confidence intervals and sample size? Greater confidence requires narrower Confidence Interval. Smaller sample size gives narrower Confidence Interval. Larger sample size gives narrower Confidence Interval. Sample size has no impact on the size of Confidence Intervals. 7. It is known that the population standard deviation of the IQ test results is 16. Assuming that we have a random sample of 135, what is the standard error of the average IQ of a sample of this size? 1.38 1.83 2.71 3.16 8. Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample standard deviation is 10.6 mmHg. What is the estimated standard error of the sample mean? 0.05 0.75 1.50 3.00 9. It is known that the population standard deviation of the IQ test results is 16. Assuming that we have a random sample of 144 and a sample mean of 98, what would be your 90% confidence interval estimate of the population mean? (Hint: use 1.65 as the critical zvalue) [89.8, 106.2] [91.8, 104.2] [93.8, 102.2] [95.8, 100.2] 10. Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample mean is 115.0 mmHg and the sample standard deviation is 10.4 mmHg. Please construct a 95% confidence interval for the population mean of students' systolic blood pressure. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical zvalue) [107.6, 122.4] [109.6, 120.4] [111.6, 118.4] [113.6, 116.4] 11. To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement? The sample size is 36 and the population proportion under null hypothesis is 25%. The sample size is 48 and the population proportion under null hypothesis is 80%. The sample size is 99 and the population proportion under null hypothesis is 90%. The sample size is 200 and the population proportion under null hypothesis is 6%. 12. In One Sample Proportion test, it is critical to understand the direction of the alternative hypothesis. What are the directions of the following two examples of alternative hypotheses? 1) Ha: P < 0.3 2) Ha: P < 0.5 1) is left tailed and 2) is right tailed. 1) is right tailed and 2) is left tailed. Both are left-tailed Both are right-tailed 13. In One Sample Proportion test, it is important to convert the sample proportion to a zscore first. In this example, we selected a random sample of size 100 from a pool of university students and asked whether they use Facebook on a regular base. Seventy replied yes. Assuming that the population proportion under the null hypothesis is 50%, what is the zscore for the sample proportion? 1.00 2.00 3.00 4.00 14. To investigate the prevalence rate of Hypertension of a certain population, we drew a random sample of 70 people from that population and among them 8 people had hypertension. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Depending on the direction of the alternative test, use 1.65 or 1.65 as the critical zvalue) Ho: P = 0.2 (Null) Ha: P < 0.2 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 15. A random sample of size 120 was selected from a pool of university students and they were asked whether they use Facebook on a regular base. Fifty replied yes. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Depending on the direction of the alternative test, use 1.65 or 1.65 as the critical zvalue) Ho: P = 0.3 (Null) Ha: P > 0.3 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 16. A group of researchers from a medical firm are trying to understand the proportion of American adults who are allergic to a medication. In a random sample of 120 adults, 15 people say they have such an allergy. For the following hypotheses, what would be your conclusion based on the information provided? The level of significance (alpha level) is 0.05. (Hint: Use 1.96 and 1.96 as the critical zvalues) Ho: P = 0.10 (Null) Ha: P 0.10 (Alternative) Reject the null hypothesis. Fail to reject the null hypothesis. Cannot conclude due to the sample size and the population proportion not meeting the requirement needed for applying Central Limit Theorem. Cannot conclude due to lack of information. 17. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred seventy three patients were recruited to participate in the clinical trial. In clinical testing, 60 out of 175 people taking the medication reported symptoms of anxiety. Of the other 198 people receiving a placebo, 80 reported symptoms of anxiety. Combining the two samples together, what is the overall proportion of those who reported symptoms of anxiety among all participants? 0.18 0.28 0.38 0.48 18. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred eighty patients were recruited to participate in the clinical trial. In clinical testing, 53 out of 200 people taking the medication reported symptoms of anxiety. Of the other 180 people receiving a placebo, 86 reported symptoms of anxiety. What is the estimated standard error of the difference of the two sample proportions based on pooled sample proportion? 0.039 0.049 0.059 0.069 19. Researchers want to test the effectiveness of a new antianxiety medication. Three hundred eighty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. In clinical testing, 50 out of 180 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 70 reported symptoms of anxiety. Do you think if the patients in the two groups performed significantly different with respect to symptoms of anxiety? Please use 0.05 as the level of significance. (Hint: use 1.96 and 1.96 as the critical z values). Yes, the proportions were significantly different. No, the proportions were not significantly different. We don't have sufficient information to conduct the test. The data do not meet the independence requirement so we cannot use a z-test. 20. Researchers want to test the effectiveness of a new antianxiety medication. Four hundred twenty patients were recruited to participate in the clinical trial and were randomly assigned to two groups, of which one received the medication, and the other, a placebo. In clinical testing, 70 out of 220 people taking the medication reported symptoms of anxiety. Of the other 200 people receiving a placebo, 105 reported symptoms of anxiety. If we use P1 to denote the population proportion of those who receive the medication and P2 of those who receive placebo, what would be your 95% Confidence Interval estimate for P1P2 based on the given information? Please note that to estimate the standard error of the difference of the sample proportions, you will use the two individual sample proportions instead of the pooled sample proportion. (Hint: Use 1.96 as your critical zvalue) [-0.299, -0.114] [-0.309, -0.104] [-0.319, -0.094] [-0.329, -0.084] 21. Thirteen undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 122.9 mmHg and 10.4 mmHg respectively. What is the obtained tscore for this sample under the null hypothesis Ho: = 120? -1.50 -1.01 1.01 1.50 22. Fourteen undergraduate students were randomly selected from a university and their systolic blood pressure was tested. The sample mean and standard deviation were 125.8 mmHg and 10.8 mmHg respectively. What would be the rejection region if you were asked to test hypotheses Ho: = 120 versus Ha: > 120 with level of significance of 0.05? Please use the attached tdistribution table to find the critical t value. t > 1.782 t > 1.771 t > 1.761 t > 2.160 23. To compare the treatment effects of two medications, two independent samples of patient performance data were collected. The sample sizes are 10 and 12 respectively. Assuming that the two populations shared the same variance, the researchers decided to conduct a two independent samples test for the means. What would be the number of degrees of freedom for the obtained t statistic with these sample sizes? 20 21 22 23 24. To compare the treatment effect of two medications, two independent samples of patient performance data were collected. The sample sizes are 10 and 12 respectively. Assuming that the two populations shared the same variance, the researchers decided to conduct a two independent samples test for the means. They found that the difference between the two sample means was 3.0 and the pooled sample standard deviation of the two samples was 3.9. What would be the obtained tvalue under the null hypothesis that assumes no difference between the two population means? 1.08 1.80 2.08 2.41 25. A random sample of 120 fifth grade students took a standardized reading test and 100 of them (83.3%) met the minimum requirement of reading proficiency for the grade level. Among these students, sixty were males and among them 45 met the requirement (75%). Among the 60 female students, fifty five met the requirement (91.7%). Their English teacher is interested to see if there is significantly difference between boys and girls regarding the proportions of passing the test. Which of the following tests would you recommend? One-sample test for proportions Two-sample test for proportions One-sample test for means Two-sample test for means