Math 2000 Practice Final Exam: Homework problems to review. Problem numbers

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1 Math 2000 Practice Final Exam: Homework problems to review Pages: Problem numbers , , , , 16 Topics: box plot, histogram, z-score, quartiles, frequency distribution chart, skewness (left/right), ogive, scatter plot, mean, standard deviation, without replacement, probability (or/and), expected value, toss a coin, area under the curve, confidence intervals, p-value, sample size, CV, TV, Ho, H1, right tail/left tail/ two tail, correlation coefficient, line of best fit, when to reject and not reject.

2 MATH 2000 Statistics Practice Final Exam 1. Given the following box plot where m is the median value, what statement could be made about the distribution of the data? A possible histogram is given with each statement a) The distribution is negatively skewed. b) The distribution is positively skewed. c) The distribution is approximately d) No statement can be made about the symmetric. data because no data values are shown. on the plot. 2. Find the z score for each student, and indicate which one is higher. Math major: X = 86, X = 90, s = 6 Physics major: X = 72, X = 76, s = 5 a) The math major has a higher score than the physics major. b) Both students have the same score. c) Neither student received a positive score; therefore, the higher score cannot be determined. d) The physics major has a higher score than the math major. 3. Find the quartiles Q 1, Q 2, and Q 3 for the following data set: 22, 47, 38, 29, 53, 26. a) Q 1 = 24, Q 2 = 20, Q 3 = 39 b) Q 1 = 26, Q 2 = 47, Q 3 = 53 c) Q 1 = 26, Q 2 = 33.5, Q 3 = 47 d) Q 1 = 22, Q 2 = 33.5, Q 3 = 53

3 4. Which distribution is correctly constructed? Classes are constructed using class limits. a) Class Freq. b) Class Freq. c) Class Freq. d) Class Fre q e) All of the above are constructed incorrectly. The following list shows a random sample of 11 students selected from a class of 30 students in a particular ABAC 1000 class. These eleven students were polled on the number of credits they are taking this semester. Refer to this data for the next two questions. 12, 15, 18, 13, 14, 14, 12, 15, 16, 18, Compute the mean or average number of credits. Round to the nearest tenth s place. a) 163 b) 14.8 c) None of these. d) 16.3 e) Calculate the standard deviation. Again, round to the nearest tenth s place. a) 2.8 b) 2.0 c) None of these. d) 1.9 e) A business has nine locations from which to choose, and they wish to rank only the top three locations. How many different ways can this be done? a) 584 b) 27 c) 84 d) 504 e) None of these. 8. A box contains a penny, a nickel, a dime, a quarter, a fifty-cent piece and a silver dollar. A coin is drawn at random and not replaced. A second coin is then drawn. For this experiment, how many outcomes are possible? a) 6 b) 12 c) 36 d) None of these. e) A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is 1, and the 5 probability of selecting a blue chip on the first draw is 5, find the probability of 16 selecting the red chip on the second draw, given that the first chip selected was a blue chip a) b) c) d) None of these. e) One thousand tickets are sold at $1 each for a color television valued at $350. What is the expected value of the gain if you purchase one ticket? 21

4 a) $0.78 b) $0.78 c) None of these. d) $0.65 e) $ A coin is tossed six times. Find the probability of getting less than three heads. Round to four decimal places. a) b) c) None of these. d) e) Find the expected value for the following distribution: x p(x) a) 10 b) 2.23 c) 11 d) 3.22 e) None of these. 13. What z value corresponds to 76% of the data less than the z value? In other words, complete the following statement: P(z < ) = Round to the nearest hundredth. a) 0.29 b) 0.71 c) 0.44 d) None of these. e) Find the area under the standard normal distribution curve between z = and z = and above the x-axis. Round to three decimal places. a) b) c) d) e) None of these. 15. The average time a person spends shopping in a supermarket is 52 minutes. If the time is normally distributed with a standard deviation of 9 minutes, find the probability that a person spends less than 59 minutes shopping. a) b) c) d) None of these. e) The average time a person spends shopping on a computer in a week is 14 hours. If the time is normally distributed with a standard deviation of 4 hours, find the probability that the mean time for a sample of 20 shoppers will be between 12 and 15 hours. a) b) c) None of these. d) e) A sample of 10 Mullet netted in a pond had a mean weight of 2.3 pounds with a standard deviation of 0.3 pounds. Find the 90% confidence interval for the mean weight of all catfish in the pond. a) 2.14 < μ < 2.46 b) 2.13 < μ < 2.47 c) None of these. d) 2.01 < μ < 2.59 e) 2.00 < μ < A survey of 600 women shoppers found that 22% enjoy shopping for shoes. What is the 95% confidence interval for the true proportion of women shoppers who enjoy shopping for shoes? Round to the nearest thousandth. a) < p < b) None of these. c) < p < d) < p < e) < p < The Academy of Orthopedic Surgeons gives a survey result that 85% of women wear shoes that are too small for their feet. A researcher wants to be 99%

5 confident that his proportion is within 4% of the true proportion. How large a sample is necessary? a) 530 b) None of these. c) 531 d) 432 e) A sample of 9 US States found that the standard deviation of life expectancy in these areas was 2.3 years. What is the 90% confidence interval for the variance of life expectancy for all the US States? Round to the nearest tenth. a) 3.2 < σ 2 < 12.1 b) 5.6 < σ 2 < 10.3 c) 2.7 < σ 2 < 15.5 d) 3.9 < σ 2 < Using Table E, what are the critical values for a two-tailed test when α = a) ±1.71 b) None of these. c) ±1.40 d) ±1.39 e) ± According to the Manly Men magazine, the national average age of a male model is now 23.2 years. A sample of 16 prospective male models in Dallas revealed that their average age was 24.6 years, with a standard deviation of 2.8 years. We may claim that the average age of male models in Dallas is greater than the national average. At α = 0. 01, what is the test value for this hypothesis test? Round to the nearest hundredth. a) 2.00 b) None of these. c) 1.93 d) 1.73 e) Bottles of coca-cola are supposed to contain 16 ounces of drink. An inspector measures 20 bottles and finds that the mean content is ounces with a standard deviation of 0.3 ounces. At α = 0. 01, can the inspector claim that the mean weight is less than 16 ounces? State the hypotheses and the decision rule (using the critical value). a) H 0: μ 16 or μ = 16 H 1 : μ < 16 0 if z < 2.33 b) None of these. H c) 0 : μ 16 or μ = 16 H 1 : μ < 16 0 if t < 2.54 d) H 0: μ or μ = H 1 : μ > if z > 2.33 e) H 0: μ or μ = H 1 : μ > if t > A recent comprehensive survey found that 71.4% of the national population owns two cars. In a random sample of 150 heads of households in a certain community, 111 responded that they owned two cars. At α = 0. 05, does this sample data indicate a difference from the national proportion? State the decision rule and compute the test statistic. a) Reject H 0 if z < 1.96 or z > 1.96; z = 0.70 b) None of these. c) Reject H 0 if z < 1.64 or z > 1.64; z = 0.70 d) Reject H 0 if z > 1.64 or z > 1.64; z = 0.70 e) Reject H 0 if z < 1.96 or z > 1.96; z = 0.70

6 For the next three questions, choose (a) for TRUE or (b) for FALSE. 25. A left-tailed test is used when H 0 : μ k or μ = k and H 1 : μ < k, where k is a constant. 26. When conducting a two-tailed z-test with α = 0. 05, the test value was The decision would be: Do not reject the null hypothesis. 27. The critical chi-square value for 10 degrees of freedom for the following figure is Compute the correlation coefficient for the following data to 4 decimal places: x y a) b) c) d) e) None of these. 29. Conduct a hypothesis test to see if there is a significant linear relationship between x and y. Use the correlation coefficient found in 28. The decision is: x y a) Do not reject the null b) Reject the null c) There is not enough information 30. Find the line of best fit for the following data with coefficients rounded to three decimal places: x y Then compute y for x = a) y = x; b) y = x; c) y = x; d) y = x; ANSWERS: B, A, C, C, B, E, D, E, C, D, A, B, B, C, C, D, B, D, C, C, E, A, C, A, A, A, B, C, B, B oh, and it says round to three decimal places nice