FINAL Exam Spring 2017 MATH 250 Elements of Statistics Multiple Choice. Due to alternate methods of computation, there may be slight differences in answer the problem number. Please do not add the "dot" (for example just type A instead of A. ). Also please to the right of the question as needed. Hypothesis testing templates are provided on the next workshe 1. Which one of the following describes a quantitative, discrete variable? A. Eye color B. Weights of new-born babies C. License plate numbers D. Number of vehicles on the Kansas Turnpike 2. A recent poll of 700 drivers on the Kansas Turnpike was conducted by selecting every 50th A. Convenience sampling B. Stratified sampling C. Systematic sampling D. Random sampling Problems 3 and 4 refer to the following data: The following are speeds (miles per hour) of cars measured with a radar gun on the Kansas Turnpike. 70 78 76 74 79 3. Find the mean and median to the nearest tenth for this sample data. A. Mean = 77, Median = 76.5 C. Mean = 77, Median = 79.0 4. Which of the following gives the sample standard deviation and the range of the data? A. SD = 3.2 B. SD = 2.8 Range = 11 Range = 9 5. A researcher obtains data by examining police records for the last ten years on violent crim A. Observational and Retrospective B. Observational and Prospective C. Experimental and Cross-sectional D. Experimental and Retrospective 6. The following frequency distribution summarizes credit rating scores for 20 randomly chosen s credit rating scores. Credit rating scores 500 - 549 550 - 599 600 - 649 650 - 699 700 - 749 750 - 799 800 - 849 A. Mean = 674.5 Frequency 1 1 1 4 5 5 3 B. Mean = 699.0 Problems 7 and 8 refer to the following histogram, which represents test scores on a recent statistics 7. Identify the percent of scores that are less than or equal to 70. A. 41.7% B. 58.3% C. 70.0% 8. Within which test score group would the first quartile (Q1) fall? A. 11-20 B. 21-30 C. 41-50 D. 51-60 Problems 9 and 10 refer to the following box-and-whisker plots that compare the pulse rates of male Male pulse rate 49 55 .......60 ..............79 Female pulse rate 52 ...66 ...... .75 84 98 9. Which distribution shape best describes the boxplot Female pulse rate? A. B. Skewed right Skewed left C. D. Uniform Normal 10. Which of the following statements is false concerning the box-and-whisker plots? A. Male pulse rate has a larger interquartile range (IQR) than the IQR of female pu B. C. D. Male pulse rate has a larger median than female pulse rate Male pulse rate has a larger maximum than female pulse rate Male pulse rate has a smaller Q3 than female pulse rate 11. Out of 40 randomly chosen patients age 65 or older, at most 20% were diagnosed to be ob A. B. C. D. Eight or fewer patients are obese. Fewer than eight patients are obese. More than eight patients are obese. None of the above. () A ) 0.07 12. IfP (P A 0.07 A. B. C. D. , which one of the following statements is false? The probability of the complement of A is 0.03 The probability of event A happening twice in a row (with replacement) is 0.004 A is not an \"unusual\" event A is not a certain event. Problems 13 and 14 refer to the following table: A marketing survey was conducted in order to determine the probability distribution for iP been created based on the results from 7 randomly chosen students from the FHSU campu represents the numbers of students who use an iPhone 6. Number of People (x) Probability 0 0.121 13. Determine the probability that all 7 students use iPhone 6 so that this data set represents a A. 0.065 B. 0.055 C. 0.045 14. Determine the expected number (mean) of students who use iPhone 6. A. 3.858 B. 2.934 C. 4.812 15. One card is randomly chosen from a standard deck of 52 cards. If the cards are drawn witho one King and an Ace card are chosen in either order? 15. One card is randomly chosen from a standard deck of 52 cards. If the cards are drawn witho one King and an Ace card are chosen in either order? 4 52A.4 51 2 4 C. 4 52 51 4 4 D. 52 51 2 4B. 4 52 51 16. Based on a poll, 60% of adults believe in the Devil. What is the probability of randomly se A. 0.26 B. 0.0026 C. 2.6 17. Assume that random guesses are made for 10 multiple choice questions on an ACT test and tha probability of success 0.35. Find the probability that the number of correct answers is at most 4 (This binomial situation.) A. 0.514 B. 0.751 C. 0.942 Problems 18 - 24 refer to the following distribution: The heights of adult males are normally distributed with a mean of 75 inches and a standard deviation 18. What is the z-score that corresponds to a height of 72 inches? A. -2.5 B. 2.5 C. -0.86 19. What symmetric interval about the mean will contain approximately 68% of the heights? A. 71.5 to 78.5 B. 65.5 to 73.5 C. 68 to 82 20. What is the probability of randomly selecting 1 male whose average height is at least 6'1\" t A. 0.7161 B. 0.6914 C. 0.9431 21. Which height is at the 60th percentile (rounded to the nearest whole number)? A. 76 B. 70 C. 72 22. What percentage of heights are between 66 inches and 74 inches? A. 15% B. 38% C. 19% 23. Suppose random samples of 16 male heights are selected repeatedly from the population. What distribution of sample means? A. Mean = 75, SD = 3.5 B. = 72, SD = 4 Mean C. D. 24. What is the probability of randomly selecting 16 males whose average height is at most 72 A. 0.0003 B. 0.9995 C. 0.8043 Problems 25 - 27 refer to the following situation: Suppose you want to determine the average home run percentage for the Royals baseball t randomly select 50 players from Royals history and determine that the mean number of ho 100 times at bat is 7.64. 25. Compute a 95% confidence interval for the mean home run percentage, given that the samp A. 7.64 1.48 B. 7.64 2.17 C. 7.64 4.17 5.61 5.61 26. Assume the population standard deviation is estimated to be How large a sample, n, should be used to obtain a margin of error of 2 with 95% confidence? A. 31 B. 45 C. 205 27. Consider the situation given in Problem #26. Which of the following would produce a conf A. Using a confidence level of 90% B. Using a smaller estimate for C. Using a larger sample size D. All of the above A-C 28. Which of the following statements is TRUE? A. B. C. D. The Central Limit Theorem states that a sampling distribution will not have the s The Central Limit Theorem states that the mean of a sampling distribution of me The Central Limit Theorem states that the standard deviation of a sampling distr will have a larger standard deviation than the population distribution from whic None of A-C is true. 29. If your population is normally distributed, which of the following statements regarding con A. B. C. D. When is known, we use the critical value z. When n 30, we use the critical value t. When n 30, we use the critical value None of A-C is always false. z. 30. POPT Popcorn is trying to determine the probability that the kernels of popcorn will pop. A ma meet this requirement at the 99% confidence level if no preliminary estimate of is known? A. 1537 B. 39 C. 4145 31. In a marketing survey, a random sample of 850 shoppers revealed that 688 remained loyal to the for the percentage of people who will remain loyal to their supermarket. .79 p .83 A. B. .84 p .91 C. 32. The US census reported that it takes workers an average of 28 minutes to drive home from wor average, more than 28 minutes to drive home from work. Which of the following gives the proper alt workers in LA to drive home from work is greater than 28 minutes? A. 28 B. 28 C. 33. According to Facebook.com, the mean number of community pages, groups, and events that us mean of 86 connections to community pages, groups, and events. Assume Compute the test H1 : 80 A. 7.98 B. -0.63 C. -1.25 34. The National Institute on Alcohol Abuse and Alcoholism reported that 45.6% of eighth-graders them had used alcohol. Is there evidence that the population proportion of eighth-graders has chang A. 0.5440 B. 0.3557 C. 0.1779 35. Suppose for a particular hypothesis test, a = 0.04 and the P value = 0.05. Which of the foll A. We reject the null hypothesis. B. We fail to reject the null hypothesis. C. The observed result is \"unusual\". D. The computed test statistic, z, does fall in the shaded critical region of the tail in the normal 36. The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) wer coefficient is the regression equation is amounts $y, where r and 0.765 3.46 1.01 x of sugar. calorie counts is 3.76. What is the best predicted calorie count for a cereal with a measured sugar am A. 3.86 calories B. 3.76 calories C. 4.23 calories 37. A correlation coefficient of 0.057 between two quantitative variables A and B indicates that A. As A increases, B tends to increase. B. Changes in A cause changes in B. C. As A increases, B tends to decrease. D. There is a very weak association between A and B, and change in A will not affect B. 38. Of the scatterplot graphs below, which one represents the strongest, negative linear correlat A. C. B. D. Problems 39 and 40 refer to the following table: The paired values represent the systolic blood pressure in the right and left arm of a patient. Right Left 102 175 101 169 94 182 79 146 39. Compute the least squares regression line for the predicted systolic blood pressure in the lef A. y 0.0579 x 2.3315 C. B. y 1.3147 x 43.565 D. 40. Calculate the correlation coefficient between the two variables. A. 0.7518 C. 0.8671 B. -0.7518 D. -0.8671 NAME: y be slight differences in answers. Choose the letter of the best answer, and type it in the blank to the left of pe A instead of A. ). Also please do not change the spacing by inserting new row. Work should be shown out re provided on the next worksheet. te variable? onducted by selecting every 50th vehicle. Identify the type of sampling method used. dar gun on the Kansas Turnpike. 79 74 78 B. Mean = 76, Median = 76.5 D. Mean = 76, Median = 79.0 n and the range of the data? C. SD = 3.2 D. SD = 2.8 77 75 Range = 9 Range = 11 he last ten years on violent crimes during Spring Breaks. Identify the types of study for this description. scores for 20 randomly chosen subjects. Estimate the mean credit rating score by using class midpoints for C. Mean = 719.5 test scores on a recent statistics test. D. Mean = 749.5 C. 70.0% 50 D. D. 38.7% 51-60 compare the pulse rates of males and females. 101 e pulse rate? C. D. Uniform Normal box-and-whisker plots? IQR) than the IQR of female pulse rate ale pulse rate st 20% were diagnosed to be obese. What is the complement of this description? ments is false? row (with replacement) is 0.0049. he probability distribution for iPhone 6 use at FHSU. A table has students from the FHSU campus. The random variable x 1 0.215 2 0.139 3 0.150 4 0.086 so that this data set represents a legitimate probability distribution. C. 0.045 D. 0.035 4.812 D. 5.146 se iPhone 6. C. ds. If the cards are drawn without replacement, what is the probability that 5 0.132 6 0.112 7 ? is the probability of randomly selecting 4 people and none of them believe in the Devil? C. 2.6 D. 0.026 questions on an ACT test and that there are 5 choices for each question with orrect answers is at most 4 (This problem meets all the requirements of a C. 0.942 D. 0.579 5 inches and a standard deviation of 3.5 inches. C. -0.86 D. 0.86 ximately 68% of the heights? C. 68 to 82 D. 64.5 to 85.5 D. 0.2838 D. 68 e average height is at least 6'1\" tall? C. 0.9431 t whole number)? C. 72 C. 19% D. 12% tedly from the population. What is the mean and standard deviation for the sampling Mean = 72, SD = 16 Mean = 75, SD = 0.875 ose average height is at most 72 inches? C. 0.8043 D. 0.1957 centage for the Royals baseball team. You mine that the mean number of home runs per percentage, given that the sample standard deviation was C. 7.64 4.17 D. s 5.21. s 5.21. 7.64 2.09 5.61 5.61 ror of 2 with 95% confidence? C. 205 D. 257 following would produce a confidence interval with a smaller margin of error? sing a larger sample size ll of the above A-C g distribution will not have the same shape as the population distribution from which it is taken. of a sampling distribution of means will have the same mean as the population distribution from which it is taken. ard deviation of a sampling distribution of means (with n 1) n 1) opulation distribution from which it is taken. owing statements regarding confidence intervals of population means is always FALSE? ernels of popcorn will pop. A margin of error of at most 2% is desired. How many kernels must be sampled to p stimate of is known? C. 4145 D. 3851 ed that 688 remained loyal to their favorite supermarkets during the past year. Find a 90% confidence interval ket. C. .87 p .98 D. .77 p .85 minutes to drive home from work. City officials in Los Angles believe that it takes workers in their city, on he following gives the proper alternative hypothesis to test the claim that the average length of time for C. 28 D. 28 pages, groups, and events that users are connected to is 80. A random sample of 64 Facebook users showed a sume Compute the test statistic for this test 48 48 C. -1.25 D. 1.00 ed that 45.6% of eighth-graders had used alcohol. A random sample of 100 eighth-graders showed that 41 of 0.05 tion of eighth-graders has changed? Use Compute the P value this test. for 0.05 C. 0.1779 D. 0.4100 value = 0.05. Which of the following statements is TRUE? l region of the tail in the normal curve. calories (per gram of cereal) were recorded for a sample of 16 different cereals. The linear correlation amounts $y, where 3.46 1.01 x of sugar. x The meanx of the 16 amounts of sugar is 0.295 grams and the mean of the 16 cereal with a measured sugar amount of 0.40 g? C. 4.23 calories riables A and B indicates that ange in A will not affect B. rongest, negative linear correlation? D. 0.295 calories d left arm of a patient. 79 144 systolic blood pressure in the left arm y 1.3147 x 43.565 y 0.0579 x 2.3315 C. 0.8671 D. -0.8671 ch it is taken. Templates for Hypothesis Testing You will want to highlight the one you need, copy it to where you are working, and then input the va calculate for you. However, you must recognize what each value represents and draw proper conc Single Sample Proportion Test: Two-tailed Proportion 0.05 0.2 1000 4860 significance level (alpha) p= x= n= q= p-hat = critical values are: test statistic = p-value = 0.8 0.2057613169 1.9599639845 and 1.0041067935 0.3153271413 -1.9599639845 Single Sample Mean Test Two-tailed Mean (sigma known) 0.01 172.5 200 119.5 40 significance level (alpha) x-bar = mu, = sigma, = n= critical values are: 2.5758293035 and test statistic = -1.4554416009 p-value = 0.1455470465 -2.5758293035 Two-tailed Mean (sigma unknown) 0.05 4.25 5 2.5 81 significance level (alpha) x-bar = mu, = s= n= critical values are: test statistic = p-value = 1.9900634213 and -2.7 0.0084591665 Inferences About 2 Proportions -1.9900634213 Two-tailed Test Given info: From Sample #1 From Sample #2 n= 56 843 27 703 alpha, = 0.05 x= p-bar = q-bar = critical values are: test statistic = p-value = 0.053686934 0.946313066 -1.9599639845 and 2.4341272112 0.0149277477 1.9599639845 Inferences about 2 Means: Independent Samples Two-tailed Test Given info: x-bar = n= s= alpha, = From Sample #1 From Sample #2 4.2 22 2.2 1.71 22 0.72 0.05 critical values are: 2.0796138447 and -2.0796138447 test statistic = 5.0453711835 p-value = 5.3852255E-005 ng, and then input the values related to the labels in red. The other values will automatically nts and draw proper conclusions based upon the resulting values. One-tailed Proportion significance level (alpha) p= x= n= q= p-hat = 0.01 0.62 1500 2500 0.38 0.6 Rt. Tailed Left Tailed critical value is: 2.326347874 or -2.326347874 test statistic = -2.0602141086 p-value = 0.0196890384 One-tailed Mean (sigma known) significance level (alpha) x-bar = mu, = sigma, = n= 0.1 182.9 200 121.8 54 Rt. Tailed Left Tailed critical value is: 1.2815515655 or -1.2815515655 test statistic = -1.0316816404 p-value = 0.1511106405 One-tailed Mean (sigma unknown) significance level (alpha) x-bar = mu, = s= n= 0.05 120 118 12 20 Rt. Tailed Left Tailed critical value is: 1.7291328115 or -1.7291328115 test statistic = 0.7453559925 p-value = 0.23258898 One-tailed Test Given info: From Sample #1 From Sample #2 n= 50 290 16 123 alpha, = 0.05 x= p-bar = q-bar = critical value is: test statistic = p-value = 0.1598062954 0.8401937046 -1.644853627 or 1.0736524347 0.1414892436 1.644853627 From Sample #1 From Sample #2 s= 0.94 21 0.31 1.65 8 0.16 alpha, = 0.05 One-tailed Test Given info: x-bar = n= critical value is: 1.8945786051 or -1.8945786051 test statistic = -8.0514648951 p-value = 4.3745228E-005