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1. Multiple choice
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(1) A survey of 158,612 job discrimination cases yielded that 33.5% of the cases were based on the race of the employees. From this data, a researcher has predicted that if 100,000 cases of job discrimination are reported next year, approximately 33,000 to 34,000 of them will be based on race. This prediction would be an example of a(n).
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| B. measurement process |
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C. statistical inference
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| D. observational study |
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| (2) A quality control engineer collects a sampling of the products coming off the assembly line and measures their weight to insure that the parts fall within customers' specifications. These specification of product characteristics are called. |
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B. measurements. |
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C. process. |
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D. variables.
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(3) The following figure is an example of a(n) ________________________ representing quantitative data.
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A. pie chart |
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B. stem-and-leaf display |
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C. dot plot |
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D. histogram
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| (4) The following figure is an example of a |
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A. class relative frequency. |
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B. stem-and-leaf display. |
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C. relative frequency histogram. |
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D. bar graph.
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| (5) If a frequency distribution is mound-shaped, symmetrical, and 95% of the measurements fall within 2 standard deviations of the mean, it can be classified by |
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A. measures of relative standing. |
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B. Chebyshev's rule. |
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C. variance. |
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D. the empirical rule.
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| (6) Find the sample z score for X=3 for the following data set. |
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3 9 8 5 7 9 4 6 |
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5 5 4 6 8 4 5 7 |
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A. -1.56 |
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B. 5.94 |
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C. -1.61 |
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D. 3.00
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| (7) The sample space for an experiment to determine who will be the next president is summarized below. What is the probability that the next president will be either Republican or Independent?
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Party
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Probability
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Republican
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0.45
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Democratic
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0.40
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Independent
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0.15
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A. 0.55 |
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B. 0.15 |
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C. 0.60 |
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D. 0.45
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| (8) Given below is the data for two popular activities. Relative age groups have been recorded for people who practice these sports regularly. Event A consists of people who plan to go biking during the summer, and event B is defined as people between the ages of 20 and 30 who either mountain bike or hike. Calculate P(A∩B) for the intersection of events A and B. |
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Age
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Hiking
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Mountain biking
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<20
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0.18
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0.21
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20-30
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0.21
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0.25
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>30
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0.34
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0.09
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A. 0.25 |
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B. 0.55 |
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C. 0.77 |
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D. 0.21 |
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| (9) Given the following probability distribution, find P(X≤4). |
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x
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1
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2
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3
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4
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5
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P(x)
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0.1
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0.2
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0.3
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0.2
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0.2
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A. 0.5 |
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B. 0.6 |
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C. 0.3 |
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D. 0.8 |
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| (10) Assuming that the number of children in the fourth grade who get an A in math each quarter has approximately a Poisson distribution, if the last term variance was 8, find the mean of the number of students who received an A in mathematics? |
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A. 2 |
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B. 6 |
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C. The answer cannot be found because of the limited amount of information supplied. |
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D. 8 |
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| (11) What assumption is made when calculating a confidence interval around the mean for a sample with less than 30 data points? |
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A. All of the choices are correct. |
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B. The sample is normally distributed. |
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C. The sample standard deviation is equal to the population standard deviation. |
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D. The population from which the sample was taken is normally distributed. |
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| (12) If a researcher finds the null hypothesis to be false when it is actually true, a(n) ______________ error is occurring? |
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A. type II |
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B. None of the choices are correct. |
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C. alternative |
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D. type I |
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| (13) A researcher wants to know whether the number of teenagers who started smoking this year is less than or greater than those who started last year. What type of test should be performed? |
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A. alternative hypothesis |
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B. two-tailed test |
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C. one-tailed test |
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D. None of the choices are correct. |
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| (14) A mechanic is concerned that his very expensive pressure gauge is giving faulty readings. He measured 18 pressures with his gauge and then compared them with the actual pressure given. His gauge showed a mean of 120 psi with a standard deviation of 0.75 psi. The actual pressure was 122 psi. For a one tailed test to see if the gauge is correct, give the value of the t test statistics. |
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A. -11.3 |
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B. -1.5 |
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C. -6.9 |
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D. -15.0 |
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| (15) The visual model shown below is referred to as a |
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A. histogram. |
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B. scattergram. |
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C. dot plot. |
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D. bar graph. |
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| 2. Calculation |
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| (1) A bicycle tire manufacturer has pumped up 20 bicycle tubes till they popped from overpressure. Given the following data for 20 failures, form a 99% confidence interval for the mean pressure before the tube fails. |
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85 87 93 94 85 92 87 91 86 94 91 89 85 88 89 87 83 85 90 88 |
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(t19,0.01/2 = 2.861) |
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(2) A manufacturer of fishing boats is trying to decide whether to concentrate their market on the east coast or the west coast. The following data for the number of families in the fishing industry that are planning to buy a boat next year for each coast has been tabulated. Calculate the standard deviation of the sampling distribution of  . |
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West Coast
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East Coast
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Number of fisherman surveyed, n1=1000
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Number of fisherman surveyed, n2=1000
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Number of fishermen planning to buy a boat,x1=83
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Number of fishermen planning to buy a boat,x2=61
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| (3) The data for a random sample of paired data is given below. Form a 90% confidence interval for μ0 ＝（sampleI –sampleII ）. (t7,0.1/2 = 1.895) |
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Pair
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SampleI
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SampleII
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1
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15
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17
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2
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17
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18
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3
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12
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13
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4
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19
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18
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5
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21
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22
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6
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14
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15
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7
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13
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12
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8
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18
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21
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| (4) A chemical engineer is running a distillation column to separate water and alcohol. The amount of pure alcohol produced from one run of the column is linearly dependent upon the original concentration of the alcohol and water solution put in the column at the beginning of the run. The column has a 50 gallon capacity. Data from five runs have been recorded. |
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Run
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Alcohol
Concentration (%)
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Pure Alcohol
Product, gallons
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1
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0.60
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28.6
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2
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0.78
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37.2
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3
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0.80
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38.3
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4
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0.43
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21.0
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5
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0.75
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36.1
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Based on upper data list, try to: |
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A. Hypothesize a model for this system with x representing the alcohol concentration, and y given by the gallons of product. |
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B. Calculate the coefficients for the regression model. |
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C. Estimate the variance,  , for the straight-line model. |
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D. Calculate the R 2 associated with this equation. |
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E. Calculate t test statistics associated with the coefficient of Alcohol Concentration (β1 ). |
