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Directions: 1) Show all work in order to receive partial credit. 2) Use any technique you wish to answer the questions on this exam unless mm in the question. Remember to check your answers when possible. 3) Use your calculator whenever possible to save yourself time and effort. 4) Read and follow directions for each question. 5) Answer each question as best you can. If you get stuck, move on to the next question and come back later. 6) if you have any questions during the exam, raise your hand and i will come to you to answer if possible. 7) GOOD LUCK TO ALL OF YOU! YOU'LL DO FlNEil none me 1:19: Emma-r mam O o ' .V Math 127 Final Exam Use the following information to answer questions 1-3. Students in an introductory statistics class were asked what type of cell phone they used. The table below shows the results for male and female students. -sss- Male 5 6 2 Female 7 4 1 1. A student is randomly selected from the class. What is the probability that an android user is selected? If necessary, round to two decimal places. (2 pts) a) 0.12 b) 0.48 c) 0.42 d) none of the above 2. A student is randomly selected from the class. What is the probability that an android user or iPhone user is selected? If necessary, round to two decimal places. (2 pts) a) 0.92 b) 0.88 c) 0.22 d) none of the above 3. A female student is selected from the class. What is the probability that she is an iPhone user? If necessary, round to two decimal places. (2 pts) a) 0.04 b) 0.16 c) 0.33 d) none of the above Math 127 Final Exam Use the following information to answer questions 4-5. In order to update its front end labor scheduling program, a supermarket chain needed to find out the amount of time necessary to bag customer orders. The following bagging times (in minutes) were recorded for 25 customer orders. 0.09 0.13 0.14 0.17 0.18 0.19 0.26 0.26 0.32 0.42 0.48 0.54 0.59 0.75 0.77 0.82 0.86 0.86 1.05 1.11 1.12 1.63 2.08 3.04 4.87 4. Find the 5-number summary for the data. DO NOT ROUND. (4 pts) 5. Construct a "modified" box plot of the bagging times showing outliers. Label the axis and scale.(5 pts)Math 127 Final Exam Use the following information to answer questions 6-7. The "Auto Sellers R Us" car dealership has been using 1-minute spot ads on a local TV station. During a 10-week period, the "Auto Sellers R Us" dealer kept a weekly record of the number of TV ads purchased versus the number of cars sold. The results are given in the following table and scatter plot: TV ads (x) 6 20 0 14 25 16 28 18 10 8 Cars sold (y) 15 31 10 16 28 20 40 25 12 15 Auto Sellers R Us 50 40 30 Cars Sol 20 10 0 5 10 15 20 25 30 TV ads 6. State the correlation coefficient. (3 pts) 7. Using the correlation coefficient and the scatterplot, explain why a linear regression would be appropriate. (2 pts) 8. If the dealership purchased 12 TV ads during a week, how many cars would we expect them to sell based on the regression line? (3 pts) Spring 2021 bage 3 of 14Math 127 Final Exam Use the following information to answer questions 9-11. A typical IQ test results in scores that are approximately normally distributed with a mean of 100 and a standard deviation of 15. Pat takes an IQ test and has an IQ of 125. 9. What percentage of the general population has an IQ at or below Pat's IQ of 125? (2 pts) a) About 17% b) About 90% c) About 95% d) About 99.7% 10. Terry's IQ is at the 98th percentile. What is Terry's IQ? (2 pts) a) About 2.05 b) About 98 c) About 131 d) About 135 11. Calculate the standard score (z-score) of Pat's IQ of 125. (2 pts) a) About -1.67 b) About 1.67 c) About 2.067 d) About 118.33 Spring 2021 age 4 of 14Math 127 Final Exam Use the following information to answer questions 12-14. The American Kennel Club (an organization that focuses on pure bred dogs) asked the following survey question in its magazine AKC Family Dog: "When choosing a pet, do you prefer cats or dogs?" Out of the 2000 people who responded to the survey, 80% answered dogs, 5% cats, and 15% had no preference. 12. Is 80% a parameter, statistic or neither? (2 pts) a) It is a parameter. b) It is a statistic. c) It is neither. 13. Is this a representative sample of all Americans? Choose the best response below. (2 pts} a) No, this has sampling bias. b) No, this has measurement bias. 0) Yes, this is a representative sample. 14. Would 80% be a good estimate of the actual percentage of all Americans that prefer dogs? (2 pts) a) No, the actual percentage would probably be higher. b) No, the actual percentage w0u1d probably be lower. 0) Yes, it would be a good estimate. Spring 2021 page 5 of 14 Math 127 Final Exam 15. Spring 2018 graduates of the Business Division at a local community college were asked about the color of the car they own. Given the following graph, answer the questions provided below: Colors of Cars for Mr B's Students 8 7 >.5| 5| =4 33' n.2I 1 I I 0 '8 C 0 '- a: "' o: E 3 9 g 3 (5 m 5 E 3 "'5' r. CarCoIor a) What type of data was collected to produce this graph, categorical or quantitative? b) How many students indicated their car was Green? c) How many total students were surveyed to produce this graph? d) What percent of students indicated that their car was Silver? e) What is the mode for this graph? Explain. f) What is the mean for this graph? Explain. Spring 2021 (1 PI) (1171') ( 2 INS) (2 pts} (2 INS) (2 P's) pageof 14 Math 127 Final Exam 16. Spring 2018 graduates of the Science Division at a local community college were asked how long they had studied for a Biology midterm. Use the following graph to answer the questions below: Hours Spent Studylng for Blology Mldterm a 7 6 g 5 S 4 E 3 2 1 o D 01 -I- -|- N M H L b 3 3 :2 3 3 E h b h a h @ Hours a) What type of data was collected to produce this graph, categorical or quantitative? (1 pt) b) What percent of students spent between 5 and 9 hours studying for the midterm? (2 pts) c) What is the maximum number of hours someone spent studying for the Biology Midterm? (1 pt) d) In which interval (or \"bar") would the median number of hours spent studying be located? (2 W) e) What is the class width used to create this histogram? (1 pt) f) Do there appear to be any outliers for this data? Explain. (2 ptS) g) How many students spent 15 or more hours studying for the exam? (2 pts) h) How many students spent 27 or loss hours studying for the exam? (2 pts) Spring 2021 page 7 of 14 Math 127 Final Exam 17. The age at graduation of the 25 Spring 2018 graduates of the Nursing Program at a local community college are listed below. 1 5 22 22 23 23 23 24 24 25 25 25 25 25 26 27 29 30 30 31 32 32 32 33 36 52 3) Calculate the mean and median for this set of data. ( 6 ptS) h) Construct a histogram with exactly SEVEN (7) classes for this data using your calculator. Copy the graph to the space below and be sure to label the graph completely. Lastly, ll in the blanks listed below with the appropriate values used to complete this histogram. (8 pts) Xmin = Ymin = Xscl = Xmax = Ymax = c) Would you describe the shape of this distribution as \"skewed right?\" Explain why or why not in a complete sentence. (2 pts) Spring 2021 page 8 of 14 Math 127 Final Exam d) Using the formal denition of an Outlier, determine the fences for this data and then state if there are any outliers present for this data. (5 pts) 18. The G.P.A.s of the Spring 2018 graduates of the Engineering Program at a local community college are given in the stem-and-leaf plot. Use this table to answer the questions below. Stern Leaves 2.7 1 2.8 2.9 4 4 5 3 .0 2 6 7 8 9 9 3.1 1 3 8 3.2 1 1 1 6 3.3 2 5 7 8 8 9 Key: 2.9|4 means GPA =- 2.94 a) How many graduates are there in the Engineering Program? (2 pts) b) Are there any outliers in this data? m in a complete sentence. (2 pts) c) What was the highest GPA of a graduate in Engineering? (1 pt) d) What is the mode for this data? (1 pt) e) Would you describe the shape of this distribution as being \"uniform?\" Explain in a sentence why or why not. (2 pts) Spring 2021 page 9 of 14 Math 1'27 Final Exam 19. Circle TRLJ E or FAQE for each of the following: (72 pt each, 10 pts total) T F a) If we wish to include the value "78\" in a stem-and-leaf plot of two digit numbers, the stem would be "7\" and the leaf would be ".\"8 T F b) A hypothesis test is conducted with a significance level of a = 0.05. A pvalue is computed for the sample data and pvalue = 0.0835. We should decide to reject H... T F c) Categorical data can be summarized in a boxplot. T F d) If data is normally distributed, exactly 68% of the data lies between 01 and 03. T F e) The median of a distribution can be visualized as the "balance point\" for the shape. T F f) The pvalue is the chance of getting our sample data, or something more extreme, under the assumption that the null hypothesis is true. T F 9) Suppose that after calculating a statistic from a sample it is later shown that the statistic did not equal the parameter. This proves that the sampling technique used must have been biased. T F h) In a hypothesis test, we determine the null hypothesis is \"Ho: 11 g 22.1 The direction of this test would be one-sided to the right. T F i) If we are discussing the 'shape of the distribution' we must be examining a categorical variable. T F j) A distribution is N(40, 4.7). To find the area below a score of 47 using our calculator we would type in normalodi(47,1E99,40,4.7). T F k) When conducting a hypothesis test, the original claim is always Hn. T F I) If we are given N(0,1) and P(X > a) = 0.5398, we would use the feature invNorm(0.5398,0,1) to find the value of a. T F m) A confounding variable is a variable which is not measured during a study, but which may explain the relationship between the measured variables. T F n) In a "double blind" experiment neither the subject nor the experimenter knows whether the person is receiving the treatment or the placebo. T F o) If we keep the sample size the same, increasing the confidence level will increase the size of the confidence interval. T F p) When we decrease the size of the class width in a histogram we increase the number of bars in the histogram. T F q) The field of inferential statistics allows us to move from known information about the population to making intelligent statements about unknown sample statistics. T F r) A sample set of data finds that 7:: 147 and s = 14. This means that approximately 99.7% of the data is between 133 and 161. T F 5) When we build a confidence interval, the population parameter will always be in the middle of this interval. T F t) Statistics is a science in which correct calculations will always lead to indisputable and Spring 2021' correct conclusions. page 10 of14 Math 127 Final Exam 20. In the following situation a study is described. You are asked to determine whether it is an experiment or an observational study. You are then asked to identify the population being discussed and what the treatment and outcome variables are. (4 pts) A researcher wishes to study the effects of listening to Mozart when studying college-level mathematics. A sample of 90 community college students is obtained and half study listening to Mozart and the other half study in silence. The two groups are then given the same math exam and the results are compared. i) This is a(n) experiment observational study (circle one) i) The population which this study attempts to discuss is iii) The treatment variable in this study is iv) The outcome variable in this study is Spring 2021 page 11 of 14