SLCC MATH 1040 FINAL EXAM FALL 2015

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1 SLCC MATH 1040 FINAL EXAM FALL 015 Form A NAME: INSTRUCTOR: TEST INSTRUCTIONS: This exam consists of both "multiple choice" and "free response" questions. For "free response" questions, you must support your answer with relevant work. Work for these problems must be shown on the exam. Work carefully and neatly, appropriately justifying your solutions. Partial credit may be awarded for relevant work on "free response" problems. You may not use your own notes, books, headphones, phones, nor any device that connects to the internet. Any calculator may be used and formulas are provided. You have 10 minutes to complete this exam. 1) Suppose that a study finds that the average pop song length in America is 4 minutes with a standard deviation of 1.5 minutes. It is known that song length is not normally distributed. If 100 pop songs are selected at random, find the probability that their mean length will be longer than 4.5 minutes. a b c d ) A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why? a. The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. b. The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. c. The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail. d. The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail. 1

2 3) The authors of the paper Fudging the Numbers: Distributing Chocolate Influences Student Evaluations of an Undergraduate Course (Teaching in Psychology [007]: 45-47) carried out a study to see if events unrelated to an undergraduate course could affect student evaluation. Students enrolled in statistics courses taught by the same instructor participated in the study. All students attended the same lectures and one of six discussion sections that met once a week. At the end of the course, the researchers randomly choose three of the discussion sections to be the chocolate group. Students in these three sections were offered chocolate prior to having them fill out course evaluations. Students in the other three sections were not offered chocolate. The researchers concluded that Overall, students offered chocolate gave more positive evaluations than students not offered chocolate. Is this study an observational study or an experiment? a. Observational Study because all the students attended the same lectures and discussion sections. b. Experiment, because sections were randomly chosen. c. Observational Study, because students could choose to take the chocolate or not. d. Experiment, because a treatment was applied to three sections. 4) The average number of hours spent completing statistics homework for a randomly selected group of SLCC statistics students is an example of what type of data? a. Quantitative Data b. Binomial Data c. Qualitative/Categorical Data d. Interval Data e. None of these 5) Suppose we construct a confidence interval for p, the proportion of Salt Lake Community College students who live more than 5 miles from Redwood campus. What would the effect be on the margin of error of the confidence interval if we reduced our sample size from 400 to 00? a. The margin of error would be smaller. b. The margin of error would remain the same. c. The margin of error would increase. d. It is impossible to tell from the information provided.

3 6) Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, 7% owned a bird, and the remaining households in the sample owned some other pet. Suppose that three households are selected randomly and with replacement. What is the probability that none of the three randomly selected households own a bird? a b c d e. None of these 7) A random sample of 1345 adult television viewers showed that 5% planned to watch the NCAA finals. The margin of error is 3 percentage points with a 95% confidence. Does the confidence interval support the claim that the majority of adult television viewers plan to watch the NCAA finals? Why? a. Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch the NCAA finals is between 50.5% and 53.5%. Since the entire interval is above 50%, this is sufficient evidence that the true proportion is greater than 50%. b. Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch the NCAA finals is between 49% and 55%. Since the confidence interval is mostly above 50% it is likely that the true proportion is greater than 50%. c. No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch the NCAA finals is between 50.5% and 53.5%. The lower limit of the confidence interval is just too close to 50% to say for sure. d. No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch the NCAA finals is between 49% and 55%. The true proportion could be less than 50%. 3

4 8) The following relative frequency histogram and table display the square footage for 40 homes sold in Dutchess County, New York. Area Relative Frequency i. What is the class width? ii. What percentage of homes sold had less than 500 square feet? 9) A bag contains 10 white, 1 blue, 13 red, 7 yellow, and 8 green wooden balls. i. Method 1: A ball is selected from the bag, its color noted, then replaced in the bag. You then draw a second ball, note its color and then replace the ball. What is the probability of selecting red balls? Round to the nearest ten-thousandth. ii. Method : A ball is selected from the bag, its color noted, then without replacing the ball, a second ball is drawn from the bag and its color noted. What is the probability of selecting red balls? Round to the nearest ten-thousandth. 4

5 10) The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table: x px ( ) If an automobile at the inspection station were randomly selected, what would be its expected number of defective tires? 11) In the Graduating Student Survey for Salt Lake Community College (Factbook ), students responded to the question What was your primary objective in attending SLCC? as follows: 7% Improve/upgrade skills for the job I currently have 44% University/College transfer credit 14% Try to get a college degree as quickly as possible % Preparation for a job to be obtained 13% Other i. Construct a Pareto Chart appropriately displaying this data. Include correct labels for axes and a title. ii. Describe at least one advantage a Pareto Chart has over a pie chart. 5

6 1) This data from Wikipedia ( gives the caffeine concentration (mg/ounce) for eight top-selling energy drinks. Energy Drink For this set of energy drinks, i. What is the mean caffeine concentration (mg/ounces)? Report to the nearest hundredth. Caffeine Concentration (mg/ounce) Red Bull 9.6 Monster 10.0 Rockstar 10.0 Full Throttle 9.0 No Fear 10.9 Amp 8.9 SoBe Adrenaline Rush 9.5 Tab Energy 9.1 ii. What is the median caffeine concentration (mg/ounces)? Report to the nearest hundredth. iii. What is the mode caffeine concentration (mg/ounces)? iv. What is the standard deviation of caffeine concentration (mg/ounces)? (You may treat this as a sample of all energy drinks.) Report to the nearest hundredth. v. What is the range of caffeine concentration (mg/ounces)? Report to the nearest tenth. 13) Twenty-five percent of customers at Fresh Market use an express checkout. If we select five customers at random, what is the probability that exactly two of them use the express checkout? Round your result to the nearest ten-thousandth. 6

7 14) The article That s Rich: More You Drink, More You Earn (Calgary Herald, April 00) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will cause an increase in income? Explain why or why not using a statistical argument. 15) A study reported by the Associated Press on April 3, 00 reported that out of a representative sample of,013 American adults, 1,556 of them indicated that a lack of respect and courtesy in American society is a serious problem. Is there convincing evidence that more than 75% of American adults believe that a lack of respect and courtesy is a serious problem? Test the appropriate hypotheses using the p-value method, with a significance level of i. Null Hypothesis: ii. Alternative Hypothesis: iii. Test Statistic: iv. p-value (report to the nearest ten-thousandth): v. Conclusion about the Null Hypothesis: vi. Conclusion addressing the original claim (complete sentence): 7

8 16) The time that it takes a randomly selected job applicant to assemble a calculator has a distribution that can be approximated by a normal distribution with a mean of 10 seconds and a standard deviation of 0 seconds. The 10% of applicants with the shortest times are to be given advanced training in calculator assembly. What task time qualifies individuals for such training? Report the time to the nearest tenth of a second. Include an appropriately labeled sketch of the normal curve in your solution for this problem. 17) A manufacturer of college textbooks is interested in testing the strength of the bindings produced by a particular binding machine. Strength of the binding can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested to estimate the average force required to break the binding with a margin of error of 0.1 pound at a 95% confidence level? Assume that is known to be 0.7 pounds. 18) A city manager claims that the mean age of bus drivers in Salt Lake City is over 5 years. Both in statistics notation and in words, write the appropriate null and alternative hypotheses for testing this claim. 8

9 19) A student randomly selects 10 paperbacks at a Barnes and Noble bookstore. She finds the mean price to be $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation,. Report the confidence interval limits to the nearest cent. Assume that the price of paperback books at the bookstore follows a normal distribution. 0) The article Air Pollution and Medical Care Use by Older Americans (Health Affairs [00]: 07-14) gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States: Region Pollution Cost of Medical Care North 30.0 $964 Upper South 31.8 $96 Deep South 3.1 $968 West South 6.8 $97 Big Sky 30.4 $95 West 40.0 $899 i. Find the equation of the least squares regression line for predicting the medical cost using pollution. Report the coefficients to the nearest hundredth. ii. Use a complete sentence to interpret the slope of your regression line in the context of the data. iii. Would you use the least squares regression equation to predict cost of medical care for a region that has a pollution measure of 60.0? If so, what is the predicted cost of medical care? If not, explain why. 9

10 Descriptive Statistics Probability Statistics Formulas and Tables x = x n x = (f x) f mean s = (x x ) n 1 s = (x i x ) f i f i 1 variance = s approximate mean from a frequency table standard deviation approx. std. dev. from a frequency table Interquartile Range: IQR = Q 3 Q 1 Lower fence = Q 1 1.5(IQR) Upper fence = Q (IQR) General Addition Rule P(A or B) = P(A) + P(B) P(A and B) multiplication rule for independent events P(A and B) = P(A) P(B) multiplication rule for dependent events P(A and B) = P(A) P(B A) complement rule P(A ) = 1 P(A) n P r = n! Permutations (no elements alike) (n r)! n! n 1!n! n k! Permutations (n 1 alike, ) n C r = n! Combinations (n r)!r! Probability Distributions mean (expected value) of a discrete random variable μ = [x P(x)] standard deviation of a discrete random variable σ = [x P(x)] μ P(x) = C x n p x (1 p) n x Binomial probability μ = n p mean for a Binomial distribution σ = n p (1 p) std. dev. for a Binomial distribution Estimating a Population Parameter Proportion: pˆ E p pˆ E where E z z pˆ 0.5 n sample size, p unknown E z ˆ 1 ˆ p p 1 pˆ n E sample size, p known Mean: s x E x E where E t n z n sample size E Standard Deviation: 1 1 n s n s R L n Normal Distribution and Sampling Distributions z = x μ σ standard normal score mean of the sampling distribution of x μ x = μ std. dev. of the sampling distribution of x (std. error) σ x = σ n μ p = p mean of the sampling distribution of p σ p = p(1 p) std. dev. of the sampling distribution of p n Hypothesis Testing z pˆ p p 1 p proportion one population n x t mean one population s n Linear Correlation and Regression r = linear correlation coefficient r = ( x i x sx )(y i y sy ) n 1 y = b 0 + b 1 x estimated eqn. of linear regression line R = r coefficient of determination Residual = y y

11 B-7 Formulas and Tables by Mario F. Triola Copyright 014 Pearson Education, Inc. Ch. 13: Nonparametric Tests (x + 0.5) - (n>) z = 1n z = T - n (n + 1)>4 n (n + 1)(n + 1) B 4 z = R -m R s R = H = r s = 1 - Sign test for n 7 5 R- n 1(n 1 + n + 1) B n 1 n (n 1 + n + 1) 1 Wilcoxon rank-sum (two independent samples) 1 N(N + 1) ar 1 + R R k b - 3(N + 1) n 1 n n k Kruskal-Wallis (chi-square df = k - 1) 6Σd n(n - 1) acritical values for n 7 30: z = G -m G s G = Ch. 14: Control Charts R chart: Plot sample ranges UCL: D 4 R Centerline: R LCL: D 3 R x chart: Plot sample means UCL: x + A R Centerline: x LCL: x - A R Rank correlation p chart: Plot sample proportions p q UCL: p + 3 B n Centerline: p p q LCL: p - 3 B n Wilcoxon signed ranks (matched pairs and n 7 30) { z 1n - 1 b G -a n 1n n 1 + n + 1b (n 1 n )(n 1 n - n 1 - n ) B (n 1 + n ) (n 1 + n - 1) Runs test for n 7 0 Table A-6 Critical Values of the Pearson Correlation Coefficient r n a = a = NOTE: To test H 0 : r = 0 against H 1 : r 0, reject H 0 if the absolute value of r is greater than the critical value in the table. Control Chart Constants Subgroup Size n D 3 D 4 A !! " # $ % # & ' ' ( ) * +, & & 0 ( -. - (. ( / 1

12 B-1 Table A- Standard Normal (z) Distribution: Cumulative Area from the LEFT z and lower * * NOTE: For values of z below -3.49, use for the area. *Use these common values that result from interpolation: z score NEGATIVE z Scores Area z _Barrelfold_pp01-08.indd 1 9/6/1 9:5 AM

13 B- POSITIVE z Scores 0 z Table A- (continued) Cumulative Area from the LEFT z * * and up.9999 NOTE: For values of z above 3.49, use for the area. *Use these common values that result from interpolation: z score Area Common Critical Values Confidence Critical Level Value _Barrelfold_pp01-08.indd 9/6/1 9:5 AM

14 B-3 Table A-3 t Distribution: Critical t Values Degrees of Freedom Area in One Tail Area in Two Tails Large _Barrelfold_pp01-08.indd 3 9/6/1 9:5 AM

15 B-4 Table A-4 Chi-Square (x ) Distribution Area to the Right of the Critical Value Degrees of Freedom Source: From Donald B. Owen, Handbook of Statistical Tables. Formulas and Tables by Mario F. Triola Copyright 014 Pearson Education, Inc. Degrees of Freedom n - 1 Confidence Interval or Hypothesis Test with a standard deviation or variance k - 1 Goodness-of-Fit with k categories (r - 1)(c - 1) Contingency Table with r rows and c columns k - 1 Kruskal-Wallis test with k samples 8056_Barrelfold_pp01-08.indd 4 9/6/1 9:5 AM