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FINAL EXAM PBHE5251. US Census statistics show that college graduates make more than $254,000 more intheir lifetime than non-college graduates. If you were to question the validity ofthis observation, what would be your basis for doing so?A. Definition of a college graduateB. Work lifestyles of the populationC. Defining “lifetime”D. How the Census was taken2. The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City CollegeA. must be more than 22, since the population is always larger than the sampleB. must be less than 22, since the sample is only a part of the populationC. could not be 22D. could be larger, smaller, or equal to 223. Since a sample is a subset of the population, the sample meanA. is always smaller than the mean of the populationB. is always larger than the mean of the populationC. must be equal to the mean of the populationD. can be larger, smaller, or equal to the mean of the populationUse the following situation for Questions 4-7. Michael, Inc., a manufacturer ofelectric defibrillators, is a firm that makes 50 types of electric defibrillators . Thetable below shows the price distribution of the defibrillators .Price (In $) Number of Defibrillators100 – 130 8140 – 170 12180 – 210 20220 – 250 10TOTAL 761.22Select from the following choices for Questions 4-7. Use letter only in the blank.A. 32 B. 50% C. 20 D. 30 E. 16% F. 10 G. 60% H. 504. How many defibrillators have a price of at least $180?__ D. _____5. What percentage of the defibrillators has a price of at least $180? ___%___6. What percentage of the defibrillators has a price of less than $140? ___ E. __7. How many defibrillators cost at least $140 but no more than $210? __ A. ____8. Temperature is an example ofa quantitative variableA. a qualitative variableB. a quantitative variableC. either a quantitative or qualitative variableD. neither a quantitative nor qualitative variableUse the following situation for Questions 9 and 10.The following frequency distribution shows the frequency of outbreaks of the11 virus (statistics flu) for the following households in a small rural community.Households 1134 406 168 41 25 12 : 1786Outbreaks 0 1 2 3 4 59.Use the frequency distribution to construct a probability distribution by filling inthe blanks below.x 0 1 2 3 4 5P(x) P(0) = P(1) = P(2) = P(3) = P(4) = P(5) =10. Compute the mean and the standard deviation and select from the following the appropriate interpretation of the results (select best response)A. A household on the average has 0.9 outbreaks with a standard deviation of.6 outbreaksB. A household on the average has 0.6 outbreaks with a standard deviation of12 outbreaksC. A household on the average has 0.9 outbreaks with a standard deviation of.9 outbreaksD. A household on the average has 0.6 outbreaks with a standard deviation of.9 outbreaksUse the following situation for Questions 11 – 13.Twenty students were randomly selected for cholesterol screening. The followingdata were collected.260 164 210 225 244 254 233 184 269 206158 209 221 213 198 179 214 257 246 22111. Using the information above compute the following: (Round to nearest hundredth)A. Mean = _____B. Median = _____C. Mode = _____D. Sample Standard Deviation = _____E. The Sample Variance = ______F. The Coefficient of Variation = ______ (as a percent, for example 27.43%)12. Is the data skewed _______ (select correct letter from list below)A. No B. Skewed left C. Skewed right D. Unable to determine13. Which is the best measure of central tendency for the randomly selected cholesterolscreenings? _______ (select correct letter from list below)A. Mean B. Median C. Mode D. It does not matter, one is as good as the other14. Let event A = a patient does not survive a new treatment procedure for prostrate cancer and event B = the patient is permanently rendered sexually dysfunctional bythe new treatment. Furthermore, events A and B are mutually exclusive. Which ofthe following statements is also true?A. A and B are also independent. B. P(A or B) = P(A)P(B)C. P(A or B) = P(A) + P(B) D. P(A and B) = P(A) + P(B)15. Twenty-five percent of the employees of a large hospital are minorities. A random sample of 7 employees is selected.A. What is the probability that the sample contains exactly 4 minorities? G. 0.0577B. What is the probability that the sample contains fewer than 2 minorities? C. 0.4449C. What is the probability that the sample contains exactly 1 non-minority? F. 1.3125D. What is the expected number of minorities in the sample? I. 1.75E. What is the variance of the minorities? F. 1.3125Select from the answers below. Place the correct letter in the blanks above.A. 0.5551 B. 1.1456 C. 0.4449 D. 0.0013 E. 1.7226F. 1.3125 G. 0.0577 H. .0001 I. 1.75 J. 0.028616. The life expectancy of a lung cancer patient treated with a new drug is normally distributed with a mean of 4 years and a standard deviation of 10 months. (0.833)A. What is the probability that a randomly selected lung cancer patient will last more than 5 years? B. 11.51%B. What percentage of lung cancer patients will last between 5 and 6 years? A. 10.69% ____C. What percentage of lung cancer patients will last less than 4 years? I. 50%D. What percentage of lung cancer patients will last between 2.5 and 4.5 years?83.98 %E. If the drug manufacturer guarantees the drug will be effective for a minimum of 3years (and will pay for the entire treatment program if the patient does not survive), what percentage of lung cancer patients will have to pay for the treatment? B. 11.51% Select from the answers below. Place the correct letter in the blanks above.A. 10.69% B. 11.51% C. .0796 D. 46.01% E. 88.49%F. 68.9% G. 53.98% H. 0% I. 50% J. 0.0617217. The life expectancy in the United States is 75 with a standard deviation of 7 years.A random sample of 49 individuals is selected.A. What is the standard error of the mean? C. 1.0B. What is the probability that the sample mean will be larger than 77 years? F0.0228C. What is the probability that the sample mean will be less than 72.7 years? A. 0.0107 D. What is the probability that the sample mean will be between 73.5 and 76 years? B. 0.7745E. What is the probability that the sample mean will be between 72 and 74 years? J. 0.1573____F. What is the probability that the sample mean will be larger than 73.46 years? H. 0.9389Select from the answers below. Place the correct letter in the blanks above.A. 0.0107 B. 0.7745 C. 1.0 D. 0.8427 E. 0.9772F. 0.0228 G. 1/7 H. 0.9389 I. 22.55% J. 0.157318. The standard hemoglobin reading for healthy adult men is 15 g/110 ml with a standard deviation of = 2 g. For a group of men, we find a mean hemoglobin of 16.0 g.A. Obtain a 95% confidence interval for if the group size was 25 The calculation is as follows 16± 1.96 * 2/√25 = (15.216, 16.784)B. Obtain a 95% confidence interval for if the group size was 36__ B. 15.347 – 16.653 ___C. Obtain a 95% confidence interval for if the group size was 49 A. 15.440 – 16.560Select from the answers below. Place the correct letter in the blanks above.A. 15.440 – 16.560 B. 15.347 – 16.653 C. 14.440 – 15.560D. 14.316 – 15.684 E. 15.316– 16.684 F. 14.347 – 15.65319. Doubling the size of the sample willA. reduce the standard error of the mean to one-half its current valueB. reduce the standard error of the mean to approximately 70% of its current valueC. have no effect on the standard error of the meanD. double the standard error of the mean20. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the sample size is large is based on theA. central limit theoremB. fact that we have tables of areas for the normal distributionC. assumption that the population has a normal distributionD. None of these alternatives is correct.Use the following situation for Questions 21 – 23. In order to estimate the average time spent on the dialysis machines per kidney patient at a local university hospital, data were collected for a sample of 81 patients over a one week period.Assume the population standard deviation is 1.2 hours.21. The standard error of the mean isA. 7.5 B. 0.014 C. 0.160 D. 0.13322. With a 0.95 probability, the margin of error is approximatelyA. 0.26B. 1.96 C. 0.21 D. 1.6423. If the sample mean is 9 hours, then the 95% confidence interval isA. 7.04 to 110.96 hours B. 7.36 to 10.64 hoursC. 7.80 to 10.20 hours D. 8.74 to 9.26 hours24. The t distribution is applicable whenever:A. the sample is considered large (n 30).B. the population is normal and the sample standard deviation is used toestimate the population standard deviationC. n 100D. n 1000Use the following situation for Questions 25 – 26. A random sample of 16statistics examinations from a large population was taken. The average score inthe sample was 78.6 with a variance of 64. We are interested in determiningwhether the average grade of the population is significantly more than 75. Assumethe distribution of the population of grades is normal.25. The test statistic is: A. 0.45 B. 1.80 C. 3.6 D. 826. At 95% confidence, it can be concluded that the average grade of the populationA. is not significantly greater than 75B. is significantly greater than 75C. is not significantly greater than 78.6D. is significantly greater than 78.627. Independent samples are obtained from two normal populations with equalvariances in order to construct a confidence interval estimate for the differencebetween the population means. If the first sample contains 16 items and the secondsample contains 36 items, the correct form to use for the sampling distribution istheA. normal distributionB. t distribution with 15 degrees of freedomC. t distribution with 35 degrees of freedomD. t distribution with 50 degrees of freedomUse the following situation for Questions 28 – 33. A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. Youare given the following results.Today Five Years AgoMean 82 88Variance 112.5 54Sample Size 45 3628. The difference between the means of the two populations is (d) =A. 58.5 B. 9 C. -9 D. -629. The standard deviation of the difference between the means of the two populations isA. 12.9 B. 9.3 C. 4 D. 230. The 95% confidence interval for the difference between the two population means isA. -9.92 to -2.08B. -3.92 to 3.92C. -13.84 to 1.84D. -24.228 to 12.2331. The test statistic for the difference between the two population means isA. -.47 B. -.65 C. -1.5 D. -332. The p-value for the difference between the two population means isA. .0014 B. .0028 C. .4986 D. .997233. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)A. There is a statistically significant difference in the average finalexamination scores between the two classes.B. There is no statistically significant difference in the average finalexamination scores between the two classes.C. It is impossible to make a decision on the basis of the information given.D. There is a difference, but it is not significant.Use the following situation for Questions 34 – 38. The director of a regional hospital is interested in determining whether or not the proportion of incoming female patients who needs a pap-smear has increased. A sample of female patients taken several years ago is compared with a sample of female patients this year.Results are summarized below.Sample Size No. Requiring Pap-SmearPrevious Sample 250 50Present Sample 300 6934. The difference between the two proportions is:A. 50 B. 19 C. 0.50 D. – 0.0335. The pooled proportion has a value ofA. 0.216 B. – 0.216 C. 1.645 D. 0.536. The interest of the director represents aA. one tailed testB. two tailed testC. one tailed or a two tailed test, depending on the confidence coefficientD. one tailed or a two tailed test, depending on the level of significance37. The test statistics for this test isA. 1.645 B. 1.96 C. 0.035 D. – 0.85138. If the test is to be done with an =.05 theA. null hypothesis should be rejectedB. null hypothesis should not be rejectedC. alternative hypothesis should be acceptedD. None of these alternatives is correct.39. Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained._Y= 120 – 10 XBased on the above estimated regression equation, if price is increased by 2 units,then demand is expected toA. increase by 120 units B. increase by 100 unitsC. increase by 20 units D. decease by 20 units40. If there is a very strong correlation between two variables, then the coefficient of correlation must beA. much larger than 1, if the correlation is positiveB. much smaller than 1, if the correlation is negativeC. much larger than oneD. None of these alternatives is correct.41. Regression analysis was applied between sales (in $1000) and advertising (in $100)and the following regression function was obtained. _Y = 500 + 4 XBased on the above estimated regression line if advertising is $10,000, then thepoint estimate for sales (in dollars) isA. $900 B. $900,000 C. $40,500 D. $505,000Use the following situation for Questions 42 – 46. You are given the followinginformation about y and x.y xDependent Variable Independent Variable5 157 129 1011 742. The least squares estimate of b1 equalsA. -0.7647 B. -0.13 C. 21.4 D. 16.41243. The least squares estimate of b0 equalsA. -0.7647 B. -1.3 C. 164.1176 D. 16.4117644. The sample correlation coefficient equalsA. -86.667 B. -0.99705 C. 0.9941 D. 0.9970545. The coefficient of determination equalsA. -0.99705 B. -0.9941 C. 0.9941 D. 0.9970546. A researcher selected a sample of 50 residents from each of three different cities to determine if they were willing to participate in a medical experiment. At _ = .05, test the claim that the proportions who will participate are equal.Residents City 1 City 2 City 3Willing to participate 20 12 22Not willing to participate 30 38 28Total 50 50 50A. There is not evidence to reject the claim that the proportions are equal because the test value 4.861 < 5.991B. There is evidence to reject the claim that the proportions are equal because the test value > 1.042C. There is not evidence to reject the claim that the proportions are equal because the test value 5.991< 12.592D. There is evidence to reject the claim that the proportions are equal because the test value 5.991 > 1.04247. A researcher is comparing samples from 6 different populations. Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means are not all equal. How many of the population means would be significantly different from the others?A. Three (half) B. At least 1C. All would be different D. More than 2Use the following situation for Questions 48 – 50. A research firm reported that15% of those surveyed described their health as poor, 26% as good, 40% as verygood, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 600 people in Chicago, 70 described their health as poor, 180 as good, 210 as verygood, and 140 as excellent. Complete the chart below by filling in the observed and expected values.48. observed expected poor 70 90 good 180 156 Very good 210 240 excellent 140 114 Observed ExpectedPoorGoodVery GoodExcellent49. Calculate the test statistic ________ (to two decimal places, i.e 2.34)50. Given an = .05, what is the result of the chi-squared test?A. There is not evidence to reject the claim that the proportions are equal because the test value is less than the critical 2 value.B. There is evidence to reject the claim that the proportions are equal because the test value is greater than the critical 2 value.C. There is not evidence to reject the claim that the proportions are equal because the test value is greater than the critical 2 value.D. There is evidence to reject the claim that the proportions are equal because he test value is less than the critical 2 value.
