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##### Statistics 40 Questions Assignment

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Question;1. In sampling without replacement from a population of 900, it's found that the standard error of the mean ox, is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?A. 400B. 600C. 200D. 5002. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?A. 18.3, 95%B. 18.3, 0.95C. 20.3, 95%D. 20.3, 0.953. Determine the power for the following test of hypothesis.H0:? = 950 vs. H1:?? 950, given that? = 1,000,? = 0.10,? = 200, and n = 25.A. 0.6535B. 0.5062C. 0.3465D. 0.49384. What is the rejection region for a two-tailed test when? = 0.05?A. |z | > 1.96B. z > 2.575C. |z | > 1.645D. |z | > 2.5755. What is the purpose of sampling?A. To achieve a more accurate result than can be achieved by surveying the entire populationB. To verify that the population is approximately normally distributedC. To create a point estimator of the population mean or proportionD. To estimate a target parameter of the population6. Which of the following statements about p-value testing is true?A. P-value testing uses a predetermined level of significance.B. The p represents sample proportion.C. The p-value is the lowest significance level at which you should reject H0.D. P-value testing applies only to one-tail tests.7. H0 is p = 0.45 and H1 is p? 0.45. What type of test will be performed?A. Two-tail testing of a proportionB. One-tail testing of a meanC. Two-tail testing of a meanD. One-tail testing of a proportion8. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the p-value you would report for this test?A. 0.4963B. 0.0074C. 0.0041D. 0.00379. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm's employees?A. 30B. 4C. 3D. 2.510. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected. 68, 79, 70, 98, 74, 79, 50, 102, 92, 96 Based on this information, the confidence level would be 90% that the population mean is somewhere betweenA. 73.36 and 88.24.B. 69.15 and 92.45.C. 71.36 and 90.24.D. 65.33 and 95.33.11. The commissioner of the state police is reported as saying that about 10% of reported auto thefts involve owners whose cars haven't really been stolen. What null and alternative hypotheses would be appropriate in evaluating this statement made by the commissioner?A. H0: p? 0.10 and H1: p > 0.10B. H0: p = 0.10 and H1: p? 0.10C. H0: p? 0.10 and H1: p 0.10 and H1: p? 0.1012. A portfolio manager was analyzing the price-earnings ratio for this year's performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for the manager to use in this situation?A. Because ?2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average price earnings ratio for the stocks is less than 20.B. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.C. If z > 2.33, reject H0.D. If t > 2.68 or if t < ?2.68, reject H0.13. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?A. ?2.64B. ?2.68C. 2.64D. 2.6814. A woman and her son are debating about the average length of a preacher's sermons on Sundaymorning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?A. 3.32B. 0.95C. ?3.32D. 6.6915. When the confidence coefficient is large, which of the following is true?A. It's more likely that the test will lead you to reject the null hypothesis.B. Its value is close to 1.0, but not larger than 1.0.C. The confidence interval is narrow.D. Its value is 1.0 or larger.16. Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that s = $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices?A. 15B. 8C. 4D. 1617. Which of the following statements correctly compares the t-statistic to the z-score when creating aConfidence interval?A. You can use t all the time, but for n? 30 there is no need, because the results are almost identical if you use t or z.B. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.C. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.D. Use t when the sample size is small, and the resulting confidence interval will be narrower.18. In a criminal trial, a Type II error is made when a/anA. innocent person is convicted.B. guilty defendant is convicted.C. guilty defendant is acquitted.D. innocent person is acquitted.19. Nondirectional assertions lead only to _______-tail tests.A. oneB. rightC. twoD. left20. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?A. The researcher should use the z-test because the population is assumed to be normally distributed.B. The t-test should be used because the sample size is small.C. The t-test should be used because? and? are unknown.D. The researcher should use the z-test because the sample size is less than 30.21. Lily Energy Systems manufacturer's wood-burning heaters and fireplace inserts. One of its systems has an electric blower, which is thermostatically controlled. The blower is designed to automatically turn on when the temperature in the stove reaches 125?F and turn off at 85?F. Complaints from customers indicate that the thermostat control is not working properly. The company feels that the thermostat is acceptable if the variance in the cutoff temperature is less than or equal to 175. The company takes a sample of 24 thermostats and finds that the variance equals 289. The calculated chi-square test statistic and the table value for a 0.05 significance level areA. 38.076, 38.99.B. 35.172, 38.99.C. 37.983, 38.076.D. 37.983, 35.172.22. What is the slope of the line that passes through the points (?5,?8) and (3,8)?A.?2B.??C. 2D. ?23. Another name for the residual term in a regression equation isA. random error.B. pooled variances.C. homoscedasticity.D. residual analysis.24. A balanced experiment requires thatA. at least one sample equal size is 30.B. the number of treatments equals the number of samples.C. an equal number of persons or test units receives each treatment.D. at least two treatment groups be used.25. A left-tail area in the chi-square distribution equals 0.95. For df = 10, the table value equalsA. 18.307.B. 20.483.C. 3.940.D. 15.987.26. In testing the difference between two population means using two independent samples, we use thepooled variance in estimating the standard error of the sampling distribution of the sample mean difference x?1? x?2 if theA. populations are nonnormal with unequal variances.B. ample sizes are both large.C. sizes are both greater than 30.D. populations are at least normally distributed with equal variances.27. Consider the following data values of variables x and y.Find the least squares regression line. x 4 2 6 4 3 y 5 3 7 6 5A.?1.045 + 0.932xB. 21.206 + 1.073xC. 1.122 + 1.073xD. 1.659 + 0.932x28. The object on which the response and factors are observed is calledA. factors.B. experimental unit.C. treatments.D. factor level.29. A random sample of males and females involved in rear-end accidents results in the following Minitab summary: What is the standard error of the statistic between the two means? N MEAN MEDIAN TRMEAN STDEV SEMEANFEMALES 33 23.91 20.00 23.38 9.77 1.70MALES 38 28.87 28.50 28.44 9.67 1.57A. 0.897B. 4.96C. 1.635D. 2.31430. In testing a population variance or constructing a confidence interval for the population variance, anessential assumption is thatA. the population is normally distributed.B. sample size exceeds 30.C. expected frequencies equal or exceed 5.D. the population is uniformly distributed.31. With larger and larger numbers of categories in chi-square tests, the chi-square distribution takes on the shape of the _______ distribution.A. binomialB. normalC. t-D. Poisson32. An indication of no linear relationship between two variables would be a coefficient ofA. correlation of 0.B. determination equal to?1.C. determination equal to 1.D. correlation equal to?1.33. The F-statistic in a one-way ANOVA represents the variationA. between the treatments plus the variation within the treatments.B. within the treatments divided by the variation between the treatments.C. between the treatments divided by the variation within the treatments.D. within the treatments minus the variation between the treatments.34. Given the significance level 0.025, the F-value for the degrees of freedom, df = (7,3) isA. 5.89.B. 27.67.C. 14.62.D. 8.45.35. In using the ANOVA models, the assumptions made about the data areA. all 3 assumptions made here about the data.B. the samples are independent.C. the population variances are equal.D. the population distributions are normal.36. In testing for the equality of two population variances, when the populations are normally distributed, the 10% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area ofA. 0.10.B. 0.20.C. 0.05.D. 0.90.37. The vertical distances between observed and predicted values of y are calledA. errors of prediction.B. least square lines.C. scatterplots.D. methods of least squares.38. In a hypothesis test for the population variance, the alternate hypothesis is the population variance does not equal 17.0. The significance level to be used is 0.05 and the sample size to be taken is 25. The table value(s) to use from the chi-square distribution is/areA. 12.401 and 39.364.B. 40.647.C. 13.120 and 40.647.D. 39.364.39. Given the significance level 0.05, the F-value for the degrees of freedom, df = (3,7) isA. 4.12.B. 4.35.C. 6.16.D. 8.89.40. A "best-fit" mathematical equation for the values of two variables, x and y, is calledA. correlation analysis.B. errors of prediction.C. scatter diagram.D. regression analysis.

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