Final Exam with numbers and answer choices removed Module # in red below The numbers given were replaced by X1, X2, X3, etc 1. Find the number of successes X1, suggested by the given statement: A computer manufacturer randomly selects X2 of its computers for quality assurance and finds that X3% of these computers are found to be defective. 2 2. In the scatter diagram below, is the data point, P, an outlier, an influential point, both, or neither? 9 3. Given the numbers below determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution or neither. 5 4. Assume that the data has a normal distribution and the number of observations is greater than X1. Find the critical z value used to test a null hypothesis. = 0.05 for a left-tailed test. 2 5. Use the given information to find the coefficient of determination. Find the coefficient of determination, given that the value of the linear correlation coefficient, r : ... 8 6. Identify the null hypothesis and the alternative hypothesis . A cereal company claims that the means weight of the cereal in its packets is X1 oz. 5 7. Find the margin of error for the 95% confidence interval used to estimate the population proportion. Given n and x 4 8. Use the given information to find the P-value. The test statistic in a right-tailed test is z=... 4 9. A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of x people, she obtains the following 99% confidence interval for the population proportion p X1 < p < X2 Which of the statements below is a valid interpretation of this confidence interval? 6 10. Determine whether the samples are independent or consist of matched pairs (dependent samples). The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug. 7 11. Use the given data table for x and y to find the equation of the regression line. Round the final values to three significant digits, if necessary. 9 12. A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects X1 students from each college and records the number that smoke. The results are shown below. 10 College A College B College C College D Smoke Don't smoke Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges if the test statistic: 2 = .... 13. Compute the test statistic used to test the null hypothesis that . In a vote on the Clean Water bill, X1% of the 205 Democrats voted for the bill while X2% of the 230 republicans voted on the bill. 6 14. Assume that you want to test the claim that the paired data come from a population for which the mean difference is . Compute the value of the test statistic. x y 7 15. X1 randomly selected light bulbs were tested in a laboratory and X2 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours. 2 16. The two data sets are dependent. Find to the nearest tenth. 7 x y 17. Use the given margin of error, confidence level, and standard deviation s to find the minimum sample size required to estimate an unknown population mean . 2 18. The regression equation relating to attitude rating(X1) and job performance rating (X2) for the employees of a company is (equation). Ten pairs of data were used to obtain the equation. The same data yield r = 0.863 and . What is the best predicted job performance rating for a person whose attitude rating is X 3 ? 9 19. Use the confidence level and sample data to find the margin of error E. College students' annual earnings: 99% confidence n = X1, =X2, s = X3 2 20. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = X1, x = X2 X3 percent 2 21. Identify the null hypothesis H0 and the alternative hypothesis H1. A researcher claims that X1% of voters favor gun control. 4 22. Do one of the following, as appropriate: (a) find the critical value z/2 (b) find the critical value t/2 (c) state that neither the normal nor the t distribution applies. X1% n = X2 s is unknown population appears to be normally distributed. 2 23. Assume that a hypothesis is test of a given claim will be conducted. Identify the type I error for the test. 4 24. Find the critical value z/2 that corresponds to a degree of confidence of X1%. 2 25. Given the linear correlation coefficient r and the sample size n, determine the critical value of r and use your finding to state whether or not the given r represents a significant linear correlation. 8 26. Use the confidence level and sample data to find a confidence interval for estimating the population m. A group of X1 randomly selected students have a mean score of X2 with a standard deviation of X3 on a placement test. What is the 90 percent confidence interval for the mean score, m, of all students taking the test? 5 27. Find the Critical Value(s) of 2 based on the given information below 3 28. A medical school claims that more than X1% of its students plan to go onto general practice. It is found that among a random sample of X2 of the school's students, that X3% of them plan to go into general practice. Find the P-value for a test of the school's claim. 4 29. From the sample statistics below of n1, n2, x1 and x2, find the value of test statistic used to test the hypothesis that the population proportions are equal. 6 30. Find the minimum sample size you should use to assure that your estimate of of error around the population p. Margin of error: X1 confidence level X2% from a prior study, estimated by X3 2 will be within the required margin 1. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 165, x = 138; 95 percent 2. Find the critical value z/2 that corresponds to a degree of confidence of 98%. 3. Use the given information to find the P-value. The test statistic in a right-tailed test is z = 1.43. 4. A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below. Smoke Don't smoke College A 17 83 College B 26 74 College C 11 89 College D 34 66 Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges if the test statistic: 2 = 17.832. 5. From the sample statistics, find the value of used to test the hypothesis that the population proportions are equal. 6. Identify the null hypothesis and the alternative hypothesis . A cereal company claims that the means weight of the cereal in its packets is 14 oz. 7. A medical school claims that more than 28% of its students plan to go onto general practice. It is found that among a random sample of 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim. 8. Is the data point, P, an outlier, an influential point, both, or neither? 9. Use the given information to find the coefficient of determination. Find the coefficient of determination, given that the value of the linear correlation coefficient, r is -0.721. 10. Determine whether the samples are independent or consist of matched pairs (dependent samples). The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug. 11. Identify the null hypothesis H0 and the alternative hypothesis H1. A researcher claims that 62% of voters favor gun control. 12. Use the confidence level and sample data to find the margin of error E. College students' annual earnings: 99% confidence; n = 74, = $3967, s = $874 13. Given the linear correlation coefficient r and the sample size n, determine the critical value of r and use your finding to state whether or not the given rrepresents a significant linear correlation. Use a significance level of 0.05. r = -0.568, n = 25 14. The two data sets are dependent. Find x 12.9 11.3 10.7 12.9 12.9 to the nearest tenth. y 12.6 12.6 10.0 10.7 12.3 15. Use the confidence level and sample data to find a confidence interval for estimating the population m. A group of 56 randomly selected students have a mean score of 30.8 with a standard deviation of 4.5 on a placement test. What is the 90 percent confidence interval for the mean score, m, of all students taking the test? 16. Find the margin of error for the 95% confidence interval used to estimate the population proportion. n = 163, x = 96 17. Find the critical value or values of information. based on the given 18. Assume that a hypothesis is test of a given claim will be conducted. Identify the type I error for the test. 19. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution or neither. Claim: = 977. Sample data: n = 25, , s = 25. The sample data appear to come from a normally distributed population with = 28. 20. Find the minimum sample size you should use to assure that your estimate of will be within the required margin of error around the population p. Margin of error: 0.04; confidence level: 99%; from a prior study, estimated by 0.13 21. Find the number of successes x suggested by the given statement. A computer manufacturer randomly selects 2360 of its computers for quality assurance and finds that 2.54% of these computers are found to be defective. 22. Compute the test statistic used to test the null hypothesis that . In a vote on the Clean Water bill, 41% of the 205 Democrats voted for the bill while 40% of the 230 republicans voted on the bill. 23. Assume that the data has a normal distribution and the number of observations is greater than 50. Find the critical z value used to test a null hypothesis. = 0.05 for a left-tailed test. 24. A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the population proportion p: 0.113 < p < 0.171 Which of the statements below is a valid interpretation of this confidence interval? 1-There is a 99% chance that the true value of p lies between 0.113 and 0.171. 2-If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and 0.171. 3-If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p. 4-If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value 25. 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours. 26. Assume that you want to test the claim that the paired data come from a population for which the mean difference is Compute the value of the test statistic. x y 11 8 5 7 13 9 5 6 . 9 4 27. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. 28. Use the margin of error, confidence level, and standard deviation s to find the minimum sample size required to estimate an unknown population mean . Margin of error: $139, confidence level: 95%, s = $513 29. Do one of the following, as appropriate: (a) find the critical value za/2 (b) find the critical value ta/2 (c) state that neither the normal nor the t distribution applies. 99%; n = 17; s is unknown; population appears to be normally distributed. 30. The regression equation relating to attitude rating(x) and job performance rating (y) for the employees of a company is . Ten pairs of data were used to obtain the equation. The same data yield r = 0.863 and . What is the best predicted job performance rating for a person whose attitude rating is 70