Macomb Community College Department of Mathematics. Review for the Math 1340 Final Exam

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1 Macomb Community College Department of Mathematics Review for the Math 0 Final Exam WINTER 0

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3 MATH 0 Practice Final Exam MATH 0 DEPARTMENT REVIEW FOR THE DEPARTMENT FINAL EXAM The Department Final Exam will have 0 multiple-choice questions. There is only ONE correct answer. The time limit for Department Final Exam is 0 minutes. All students must take the Department Final Exam on the last day of class. The student needs to purchase a RED scantron (Form No. X--PAR-L) from MCC s bookstore (located in Building P) for Department Final Exam. The student will need a # pencil for Department Final Exam. No scratch paper may be used during the Department Final Exam. You may write in the final exam packet. There is plenty of room for doing your work on the final exam. A Formula Packet will be attached to the Department Final Exam. It s the same as the formulas and tables near the end of this review. A scientific calculator or a TI- or a TI- graphing calculator may be used on the Department Final Exam. No qwerty keyboards, such as the TI-. Check with your instructor to make sure you have a permissible calculator. All cell phones and electronic devices must be POWERED OFF and put away during final exam. ANSWERS TO REVIEW QUESTIONS ARE ON THE LAST PAGE WI0 Math0PF/lm Page of

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5 Part I Assessment MATH 0 Practice Final Exam. What is a level of measurement that consists of classifying data into mutually exclusive categories in which no order or ranking can be imposed? a. nominal level b. ordinal level c. interval level d. ratio level. A numerical measurement that describes a sample is called a: a. parameter b. statistic c. population d. inference. If the bar graph for qualitative data is created by arranging the bars in order of frequency from high to low, then the graph is a: a. pie chart b. histogram c. time series d. box-plot e. pareto chart. Which parameter is NOT a measure of central tendency? a. mean b. median c. mode d. standard deviation e. Q, the second quartile. The mean of a distribution of test scores is and the standard deviation is. We plan to curve the exam by adding seven points to each score. How will this change the mean and standard deviation of the distribution? a. Both the mean and standard deviation of the distribution will be increased by seven points. b. The mean of the distribution will be increased by seven points, but the standard deviation will remain unchanged. c. The mean will be unchanged, but the standard deviation will increase by seven points. d. Neither the mean nor the standard deviation will be changed. WI0 Math0PF/lm Page of

6 MATH 0 Practice Final Exam. The mean and standard deviation of the sample data set,,,, is: a. only the mean can be computed b. µ = and σ = c. x = and s = d. x = and s = e. x = and s =. The sample data set,,,,, 00 contains an extreme value. Which measure of center is influenced the most by the extreme value? a. mean b. median c. mode d. midrange e. mean and midrange. A drawer contains black socks, brown socks, and white socks. If a sock is selected at random, find the probability that it is white. a. / b. / c. / d. /. The probability that a person will get a cold this year is 0.. If people are selected at random, find the probability that all will get a cold this year. a.. b. 0. c. 0.0 d Assume that a procedure yields a Binomial Probability Distribution with n = 00 trials and the probability of success for one trial is p = 0.. Use the given values of n and p to find the standard deviation. a. σ =.0 b. σ =. c. σ = 0. d. σ = 0 WI0 Math0PF/lm Page of

7 MATH 0 Practice Final Exam. Assume a Binomial Probability Distribution: Forty percent of the population have brown eyes. If people are randomly selected, find the probability that at most of them have brown eyes. a. P(at most ) = 0.00 b. P(at most ) = 0.0 c. P(at most ) = 0.0 d. P(at most ) = 0.00 e. P(at most ) = The data give in Table P satisfies all of the required conditions for a probability distribution. Table P x - 0 P (x) a. True b. False, because P ( x). c. False, because there is a negative value for x. d. False, because there is a missing value of x =.. In a standard normal distribution with µ = 0 and σ =, find the area that is greater than z =.: a.. b..0 c.. d... A sample of statistic classes yields an mean class size of x = students with a standard deviation of s = students. The % confidence interval estimate for the population mean is: a.. students < µ <. students b.. students < µ <. students c.. students < µ <. students d.. students < µ <. students e.. students < µ <. students WI0 Math0PF/lm Page of

8 MATH 0 Practice Final Exam. The lowest magnitude (strength) of linear correlation indicated between two variables is: a. r = 0. b. r = 0. c. r = 0.0 d. r = 0.0. A study investigates income level in the U.S. to determine if it is independent of region. If there are ten regions and five income levels, how many degrees of freedom are there to find the critical value for a χ test of independence? a. 0 b. c. d. e.. A study is done to determine, at the % level of significance, if traffic accidents occur with equal frequency throughout the week. Of the 0 accidents pulled from the files, the distribution of observed traffic accidents is shown below. DAY OF THE WEEK NUMBER OF ACCIDENTS Sunday Monday Tuesday Wednesday Thursday Friday Saturday What is the value of the test statistic for a a. 0.0 b..0 c. 0. d.. e.. χ Goodness-of-Fit/Multinomial test?. In the course of a game, WNBA player Cynthia Ciiper shoots free throws. Denoting shots made by H for hit and denoting missed shots by M, her results are as follows: H, H, H, M, H, H, H, H, M, M, M, H Use a 0.0 significance level to test for randomness in the sequence of hits and misses. a. Test statistic: G =, Critical Values and ; Reject H 0 b. Test statistic: G =, Critical Values and ; Reject H 0 c. Test statistic: G =, Critical Values and ; Fail to Reject H 0 d. Test statistic: G = ; Critical Values and ; Fail to reject H 0 e. Test statistic: G =, Critical Values and ; Fail to reject H 0 WI0 Math0PF/lm Page of

9 MATH 0 Practice Final Exam. Given below are the sample means for fifteen samples of five students each. Assume that the mean of the sample means is ten and the computed values for UCL and LCL of the x chart are fifteen and five respectively. Construct an x chart. Is this process in statistical control? Sample Mean a. The process is in statistical control. b. The process is not in statistical control, because there are eight consecutive points all above or below the centerline. c. The process is not in statistical control, because there is a point lying beyond the upper or lower control limit. d. The process is not in statistical control, because there is a pattern, trend, or cycle that is obviously not random. e. The process is not in statistical control, because more than one of the answers b, c, and d are correct. WI0 Math0PF/lm Page of

10 MATH 0 Practice Final Exam Part II 0. Which of the following data sets measure attributes that are qualitative (categorical)? a. heights b. weights c. colors d. test scores. Creating a sample of students by starting with the second name in the student directory and selecting every th name best describes what kind of sampling method? a. random b. cluster c. stratified d. systematic e. None of these. A researcher wants to determine what percent of all first graders still believe in Santa Claus. He decides to use the first graders at Warren Holland Elementary School, which is where his son goes, as his sample. The sampling technique used by this researcher is: a. random sampling b. convenience sampling c. systematic sampling d. stratified sampling e. simple random sampling. A town obtains current employment data by polling,000 of its citizens this month. Identify the type of observational study. a. Prospective b. Retrospective c. Cross-sectional d. None of these. Use the frequency distribution table below to find the value of the mean. CLASS Frequency 0 0 The mean is: a. b. 0 c.. d.. e.. WI0 Math0PF/lm Page of

11 MATH 0 Practice Final Exam. The percent of values in a data set that lie between the first (lower) quartile and the third (upper) quartile is: a. % b. % c. 0% d. 0%. If the standard deviation for a set of data is, then the variance is: a. b. c. d.. A distribution has a range of. The lowest score is. The highest score is: a. 0 b. c. d.. Sally s z-score for her test was.. Her actual score was. The class standard deviation was.. What was the mean of the test? a. 0. b.. c.. d... The approximate percentage of values in a data set that will fall between the th percentile and the th percentile is: a. % b. % c. % d. % 0. There are 0 statistic students at Macomb Community College who have a mean grade point average of. and a standard deviation of 0.. Which of the following grade point averages would be an unusual grade for statistic students at MCC? a.. b.. c.. d.. e. all of the above WI0 Math0PF/lm Page of

12 MATH 0 Practice Final Exam. The Locator formula is L = (k/0)n. The value of the third quartile Q for the data set summarized by this stem and leaf plot is: a. b. c.. d. e. none of these Stem Leaf The mode for the data set summarized by this stem and leaf plot is: a. 0 and b. c. d. e. and Stem Leaf A sample of children has a mean weight of 0 pounds and a standard deviation of pounds. If one of the children has a z-score of z =., find his weight. a. x = 0 pounds b. x = pounds c. x = 0 pounds d. There is not enough information to answer this item.. The batting average of the Macomb College baseball team is normally distributed with a mean of. and a standard deviation of.0. If John is at the th percentile, find his batting average. a.. b.. c.. d... Which of the following probabilities for an event A suggest that event A can be considered an unusual event? a. P(A) = 0.0 b. P(A) = 0. c. P(A) = 0.0 d. P(A) = 0. e. all of the above WI0 Math0PF/lm Page of

13 MATH 0 Practice Final Exam. Joe is dealing you a three-card hand from a standard deck of cards, four of which are aces. The probability that Joe will deal you exactly three aces is: a. b. c. d. 0. In a recent survey of TV watching at :00 PM on Sunday night, people watched ABC, people watched NBC, and people watched CBS. If a person is picked at random, what is the probability that the person watched NBC or CBS? a. / b. 0/ c. / d. / e. None of these. Two dice are rolled. What is the probability of getting a or? a. / b. / c. / d. /. A card is drawn from a standard deck of cards. What is the probability of getting a red king? a. / b. / c. / d. / WI0 Math0PF/lm Page of

14 MATH 0 Practice Final Exam 0. Winning a Power Ball lottery jackpot requires that you select the correct five numbers between and 0 inclusive and, in a separate drawing, you must also select the correct single number between and 0 inclusive. Find the probability of winning the jackpot. a.,, 00 b.,, 0 c.,0, 00 d.,,. If P(A) = 0., P(B) = 0., and the events A and B are independent, then P(A or B) is: a. 0. b. 0.0 c. 0. d. 0.. Events that cannot occur simultaneously are called: a. random b. independent c. mutually exclusive d. binomial. A family has children. How many different gender sequences are possible? a. b. c. d.. Provide a written description of the complement of the given event: At least one of the CD s is bad. a. All of the CD s are good. b. At least one of the CD s is good. c. None of the CD s are good. d. All of the CD s are bad. e. At least two of the CD s are bad. WI0 Math0PF/lm Page of

15 . Consider the Probability Distribution: MATH 0 Practice Final Exam x - 0 P(x) The mean or expected value is: a. 0.0 b..0 c.. d..0. Consider the Probability Distribution: The variance is: a. 0.0 b.. c.. d..0 x - 0 P(x) Which of the following is not a characteristic of a Binomial experiment? a. A fixed number of trials. b. The probability of success is the same for each trial. c. The outcome of each trial is independent of the outcome of any other trial. d. The probability of success always equals the probability of failure.. In a standard normal distribution with µ = 0 and σ =, find the area that is less than z =.: a. 0.0 b. 0.0 c. 0. d. 0.. Assume values are normally distributed with a mean of ten and a standard deviation of two. The probability that a randomly selected value lies between seven and nine is: a. 0. b. 0.0 c. 0. d. 0.0 WI0 Math0PF/lm Page of

16 MATH 0 Practice Final Exam 0. Use the normal distribution to approximate the desired binomial probability. Merta reports that % of its trains are on time. A check of 0 randomly selected trains shows that of them arrived on time. Find the probability that among the 0 trains, or fewer arrive on time. Based on the result, would it be unusual for or fewer trains to arrive on time? a..0, yes b..00, no c..00, yes d..0, no. In a standard normal distribution where µ = 0 and σ =, find the percentage of the scores that lie between z =. and z =.. a..% b. 0.% c..% d..%. All possible random samples of size n = are selected from a population with mean µ = and standard deviation σ =. The standard error of the mean σ is: x a. / b. / c. d. /. IQ scores are normally distributed with a mean of 0 and a standard deviation of. If people are randomly selected, use the Central Limit Theorem to find the probability that their mean IQ is less than. a. 0. b. 0. c. 0. d. 0.0 e The z-score that is used for a % confidence interval is: a.. b..0 c..0 d.. e..0 WI0 Math0PF/lm Page of

17 MATH 0 Practice Final Exam. Computed using the same data, a % confidence interval for a population mean is a % confidence interval for the same mean: a. wider than b. narrower than c. equal to d. less than or equal to. Given the % confidence limits for µ are and, which of the following could be the % confidence limits? a. and b. and c. and d. and e. None of these could be the % confidence limits.. How large of a sample must be taken in order to estimate the mean age of the books in a library to within months with % confidence if the standard deviation of the ages is thought to be about 0 months? a. books b. books c. books d. 0 books. The width of a confidence interval estimate for the population mean will become larger if α (alpha) is increased and the sample size and σ (sigma) remain unchanged. a. True b. False. How many dieters must be surveyed if we want to be % confident that the sample mean weight loss is within. pounds of the true population mean? Assume σ =. a. b. c. d. WI0 Math0PF/lm Page of

18 MATH 0 Practice Final Exam 0. The population is bell-shaped. The overall population standard deviation for all test scores in all of Mr. Smith s statistics class is.. A sample of test scores is found to have a mean of.. Construct a % confidence interval for the population mean. a..0 < µ <.0 b.. < µ <. c.. < µ <. d.. < µ <.. If you are using a t-test when testing a claim about a population mean and the sample size is, the degree of freedom equals: a. b. c. 0 d. None of these.. When testing a claim about the mean, if the test statistic is in the critical region, then the null hypothesis is: a. rejected b. impossible c. not rejected. Given: H 0 : µ = H : µ x = n = s = Which test statistic would be appropriate to test the null hypothesis? Assume a normal distribution if necessary. a. z-statistic b. t-statistic c. Pearson r d. Chi-squared WI0 Math0PF/lm Page of

19 MATH 0 Practice Final Exam. Suppose p represents the true proportion of college freshmen who can read at the th grade level. Some educators claim that less than 0% of all college freshmen can read at the th grade reading level. Select the appropriate alternate hypothesis. a. H : p 0.0 b. H : p< 0.0 c. H : p > 0.0 d. H : p 0.0. A state inspector claims that the Mill Valley Brewery is cheating consumers by filling bottles with less than one quart ( ounces) of beer. The inspector randomly selects of these bottles, measures their content, and obtains a mean of. oz. and a standard deviation of 0. oz. Perform an appropriate hypothesis test. The state inspector would be able to: a. Reject the null hypothesis at α = 0.0 and α= 0.0. b. Reject the null hypothesis α = 0.0 but do not reject the null hypothesis at α = 0.0. c. Reject the null hypothesis at α = 0.0but do not reject the null hypothesis at α = 0.0. d. Do not reject the null hypothesis at either α = 0.0 or α = A state inspector claims that the Mill Valley Brewery is cheating consumers by filling bottles with less than one quart ( ounces) of beer. The inspector randomly selects of these bottles, measures their content, and obtains a mean of. and a standard deviation of 0. oz. Use α = 0. 0 to perform an appropriate hypothesis test. a. There is sufficient evidence to warrant rejection of the claim that the Mill Valley brewery is cheating. b. There is not sufficient evidence to support the claim that the Mill Valley Brewery is cheating. c. The sample data supports the claim that the Mill Valley Brewery is cheating.. In a survey of 0 randomly selected workers,.% got their jobs through newspaper ads. Consider a hypothesis test that uses a 0.0 significance level to test the claim that less than 0% of workers get their jobs through newspaper ads. What is the P-value? a..0 b..0 c. 0. d e. 0. WI0 Math0PF/lm Page of

20 MATH 0 Practice Final Exam. A simple random sample of four-cylinder cars and a simple random sample of six-cylinder cars is obtained. When using the samples below to test the claim that the mean braking distance of fourcylinder cars is greater than the mean braking distances of six-cylinder cars, find the alternative hypothesis. Four-cylinder Six-cylinder n = n = x =. ft x =. ft s =. s =. a. H : µ µ 0 b. H : µ µ 0 c. H : µ µ > 0 d. H µ µ 0 : <. Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings were measured before and after drug treatment, with the results given in the following table. Use the sample data to construct a % confidence interval for the mean difference between the before and after readings. SUBJECT A B C D E F G H I J K L Before After 0 a.. < µ µ <. b.. < µ µ <. c..0 < µ <. 0 d.. < µ d <. e.. µ <. < d 0. If the correlation between x and y is r = 0., which one of the following statement is true: a. The slope of the least-square regression line is m= b = 0.. b. The y -intercept of the least-square regression line is the point (0, 0.). c. low scores on x are associated with high scores on y d. low scores on x are associated with low scores on y. If the correlation coefficient is r = 0., then what type of slope will the regression line have? a. positive b. negative c. infinite d. zero WI0 Math0PF/lm Page 0 of

21 MATH 0 Practice Final Exam. The coefficient of determination, r, is a measure of a. skew. b. the amount of variation in the y variable that is explained by the regression line. c. the location of the regression line. d. the spread of the predicted values.. A regression line was calculated as yˆ =. +. x and y =.. What is the best predicted value of y when x = and r is not statistically significant? a.. b.. c.. d... A researcher surveys people, both smokers and non-smokers, to see how many times per year they have an illness requiring them to see a doctor. The categories for the columns are zero or one visit, two or three visits, and four or more visits. If the researcher wishes to test the null hypothesis at α = 0.0 that the number of illnesses per year requiring a visit to the doctor are independent of smoking, what is the critical value for the χ test of independence. a.. b.. c..0 d.. e... Given that the rank correlation coefficient for pairs of data is r s = 0., test the claim of no correlation between the two variables. Use a significance level of 0.0. a. Critical Values r s = ±.; There does not appear to be a correlation between the variables. b. Critical Values r s = ±.; There appears to be a correlation between the variables. c. Critical Values r s = ±.; There does not appear to be a correlation between the variables. d. Critical Values r s = ±.0; There does not appear to be a correlation between the variables. e. Critical Values r s = ±.0; There appears to be a correlation between the variables. WI0 Math0PF/lm Page of

22 MATH 0 Practice Final Exam. Ten luxury cars were ranked according to their comfort levels and their prices. Make Comfort Price A B C D E F G H I J Find the rank correlation coefficient and test the claim of no correlation between comfort and price. Use a significance level of 0.0. a. Test Statistic: r s =., Critical values: r s = ±., There does not appear to be a correlation. b. Test Statistic: r s =., Critical values: r s = ±., There appears to be a correlation. c. Test Statistic: r s =., Critical values: r s = ±., There does not appear to be a correlation. d. Test Statistic: r s =., Critical values: r s = ±., There appears to be a correlation. e. Since there is a tie in the ranks for luxury car E, we cannot compute a test statistic.. Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. There are positive signs, negative signs, and ties. Use the sign test with a 0.0 significance level to test the null hypothesis of no difference. a. Test Statistic: x = ; Critical Value: ; Reject no difference b. Test Statistic: x = ; Critical Value: ; Fail to reject no difference c. Test Statistic: x = ; Critical Value: ; Reject no difference d. Test Statistic: x = ; Critical Value: ; Fail to reject no difference e. Test Statistic: x = ; Critical Value: ; Fail to reject no difference. In the runs test for randomness, the underlying concept is that if the number of runs is very low or very high, then the data is probably: a. Random b. Arranged in order from low to high c. Arranged in order from high to low d. Not random e. Mutually exclusive WI0 Math0PF/lm Page of

23 MATH 0 Practice Final Exam # - #0: A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. Mathematics 0 Verbal 0. Suppose you were to use the sign test to test the claim that programmers do better on the mathematics portion of the test, select the appropriate null and alternate hypotheses. a. H 0 : The math scores are equal to the verbal scores H : The math scores are greater than the verbal scores b. H 0 : The math scores are not equal to the verbal scores H : The math scores are equal to the verbal scores c. H 0 : The math scores are equal to the verbal scores H : The math scores are less than the verbal scores. d. H 0 : The math scores are equal to the verbal scores H : The math scores are not equal to the verbal scores 0. Use the sign test to test the indicated claim that programmers do better on the mathematics portion of the test at a 0.0 level of significance. a. Test statistic: x = 0, Critical Value x = ; Fail to reject H 0 b. Test statistic: x = 0, Critical Value x = ; Reject H 0 c. Test statistic: x =, Critical Value x = 0; Fail to reject H 0 d. Test statistic: x =, Critical Value x = 0; Reject H 0 WI0 Math0PF/lm Page of

24 MATH 0 Practice Final Exam. In a manufacturing process it is required to that the mean equal ten. The LCL is computed to be five and the UCL is computed to be fifteen. Which of the following x charts illustrates a process that is in control? A B C E. More than one of these are in control. D. WI0 Math0PF/lm Page of

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26 MATH 0 Practice Final Exam Table A- Binomial Distribution N x N x WI0 Math0PF/lm Page of

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31 MATH 0 Practice Final Exam Critical Values for the Sign Test (one tail) (one tail) (one tail) (one tail) n (two tails) (two tails) (two tails) (two tails) * * * * * * * * * * * * * * * * * * * 0 * * 0 0 * * It is not possible to get a value in the critical region Reject the null hypothesis if the number of the less frequent sign (x ) is less than or equal to the value in the table For values of n >, use a normal approximation with the critical z value: n ( x +.) z = n WI0 Math0PF/lm Page of

32 MATH 0 Practice Final Exam Critical Values of Spearman's Rank Correlation Coefficient r s n alpha =. alpha =.0 alpha =.0 alpha =.0 0. * * * * * For n > 0, use r s ± z = n to test α / H0 ρs vs H : = 0. : ρ 0 s α α - -r s r s WI0 Math0PF/lm Page of

33 MATH 0 Practice Final Exam Critical Values for Number of Runs G Value Value of n of n The entries in this table are the critical G values, assuming a -tailed test with significance level alpha =.0. Reject H 0 (randomness) if the total number of runs G is less than or equal to the smaller entry in the table or greater than or equal to the larger entry in the table. WI0 Math0PF/lm Page of

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38 MATH 0 Practice Final Exam ANSWERS. A. C. B. C. E. A. D. C. B. C. E. D. E. D. D. C. C 0. C. A. D. C. D. B. A. C. D. A. A. C. C. D. A. E. B. C. B. D 0. A 0. C. C. D. A. B. B. C. B. E. B. C. C. C. D. C. C. D. E. B 0. C 0. D. A. C. B. E. B. A. A. C. D. A. A. D. E. A. D. D. A. A 0. B 0. C. B. C WI0 Math0PF/lm Page of