1. In a criminal trial, a Type II error is made when a/an
A. innocent person is convicted.
B. guilty defendant is convicted.
C. guilty defendant is acquitted.
D. innocent person is acquitted.
2. When the confidence coefficient is large, which of the following is true?
A. It's more likely that the test will lead you to reject the null hypothesis.
B. Its value is 1.0 or larger.
C. The confidence interval is narrow.
D. Its value is close to 1.0, but not larger than 1.0.
3. Which of the following statements correctly compares the t-statistic to the z-score when creating a confidence interval?
A. Using t is easier because you do not have to worry about the degrees of freedom, as you do with z.
B. You can use tall the time, but for n ≥ 30 there is no need, because the results are almost identical if you use t or z.
C. The value of z relates to a normal distribution, while the value of t relates to a Poisson distribution.
D. Use t when the sample size is small, and the resulting confidence interval will be narrower.
4. A portfolio manager was analyzing the price-earnings ratio for this year's performance. His boss said that the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally distributed, and test at the 0.01 level of significance. Which of the following is the correct decision rule for the manager to use in this situation?
A. If z > 2.33, reject H0.
B. If t > 2.68 or if t < -2.68, reject H0.
C. Because 2.81 is greater than 2.33, reject H0. At the 0.01 level, the sample data suggest that the average price-earnings ratio for the stocks is less than 20.
D. Because -2.81 falls in the rejection region, reject H0. At the 0.01 level, the sample data suggest that the average priceearnings ratio for the stocks is less than 20.
5. A mortgage broker is offering home mortgages at a rate of 9.5%, but the broker is fearful that this value is higher than many others are charging. A sample of 40 mortgages filed in the county courthouse shows an average of 9.25% with a standard deviation of 8.61%. Does this sample indicate a smaller average? Use α = 0.05 and assume a normally distributed population.
A. Yes, because the test statistic is greater than -1.645.
B. No, because the test statistic falls in the acceptance region.
C. Yes, because the sample mean of 9.25 is below 9.5.
D. No, because the test statistic is -1.85 and falls in the rejection region.
6. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic?
A. 2.68
B. 2.64
C. -2.64
D. -2.68
7. A researcher wants to carry out a hypothesis test involving the mean for a sample of n = 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct?
A. The t-test should be used because α andμ are unknown.
B. The researcher should use the z-test because the population is assumed to be normally distributed.
C. The t-test should be used because the sample size is small.
D. The researcher should use the z-test because the sample size is less than 30.
8. To schedule appointments better, the office manager for an ophthalmologist wants to estimate the average time that the doctor spends with each patient. A random sample of 49 is taken, and the sample mean is 20.3 minutes. Assume that the office manager knows from past experience that the standard deviation is 14 minutes. She finds that a 95% confidence interval is between 18.3 and 22.3 minutes. What is the point estimate of the population mean, and what is the confidence coefficient?
A. 20.3, 0.95
B. 18.3, 0.95
C. 20.3, 95%
D. 18.3, 95%
9. In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected.
68, 79, 70, 98, 74, 79, 50, 102, 92, 96
Based on this information, the confidence level would be 90% that the population mean is somewhere between
A. 71.36 and 90.24.
B. 69.15 and 92.45.
C. 65.33 and 95.33.
D. 73.36 and 88.24.
10. What sample size is required from a very large population to estimate a population proportion within 0.05 with 95% confidence? Don't assume any particular value for p.
A. 271
B. 38
C. 385
D. 767
11. Which of the following statements about hypothesis testing is false?
A. The test will never confirm the null hypothesis, only fail to reject the null hypothesis.
B. In both the one-tailed and two-tailed tests, the rejection region is one contiguous interval on the number line.
C. The rejection region is always given in units of standard deviations from the mean.
D. A Type I error is the chance that the researcher rejects the null hypothesis when in fact the null hypothesis is true.
12. If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she'll perform _______-tail testing of a _______.
A. two, proportion
B. two, mean
C. one, mean
D. one, proportion
13. What is the rejection region for a two-tailed test when α = 0.05?
A. |z | > 1.645
B. |z | > 2.575
C. z > 2.575
D. |z | > 1.96
14. A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm's employees?
A. 2.5
B. 30
C. 4
D. 3
15. The power of a test is the probability of making a/an _______ decision when the null hypothesis is
_______.
A. incorrect, true
B. correct, false
C. incorrect, false
D. correct, true
End of exam
16. A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?
A. 3.32
B. 0.95
C. -3.32
D. 6.69
17. H0 is p = 0.45 and H1 is p ≠ 0.45. What type of test will be performed?
A. One-tail testing of a mean
B. Two-tail testing of a mean
C. Two-tail testing of a proportion
D. One-tail testing of a proportion
18. Nondirectional assertions lead only to _______-tail tests.
A. right
B. left
C. two
D. one
19. A human resources manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.
A. 63.14 to 85.26
B. 68.72 to 79.68
C. 64.92 to 83.48
D. 13.64 to 134.76
20. Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean is not equal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the p-value you would report for this test?
A. 0.0037
B. 0.0074
C. 0.0041
D. 0.4963
21. A particular sample contains 50 data values. According to Chebyshev's theorem, which of the following is the number of values you would expect to fall within 3.0 standard deviations of the mean?
A. 35
B. 25
C. 5
D. 45
22. To answer the question, refer to the following list of raw data.
63, 71, 72, 77, 77, 78, 86, 77, 88, 88
What is the mean for the data?
A. 88
B. 77.5
C. 77.7
D. 77
23. Use the following data sample to answer the question.
4, 14, 6, 9, 21, 3, 7, 10
What is the standard deviation of this data sample?
A. 5.90
B. 4.31
C. 34.79
D. 243.5
24. To answer the question, refer to the following data.
Ten students were sampled at random from a student population. Each was asked how many courses he or
she was planning on studying in the upcoming year. The following is a list of the reported data values: 1, 2,
2, 3, 4, 5, 5, 5, 5, 6
What is the variance for the data values?
A. 2.56
B. 1.687
C. 1.6
D. 2.844
25. Which of the following statements is true?
A. In a true census, no inferential statistics can be done, because the entire population is the sample.
B. The definition of a census is the decennial census of the United States of America.
C. When taking a sample from the population, the variable involved will always be qualitative.
D. A population is the object upon which we collect data.
26. Which of the following statements is true about a stem-and-leaf plot?
A. It uses vertical bars to illustrate a probability distribution.
B. It involves creating columns of dots, one for each datum in the sample.
C. Stem-and-leaf plots are histograms whose bars have been arranged in decreasing order of frequency.
D. It separates data at the decimal point, creating horizontal rows whose values are close together.
27. If a great many data values cluster to the left of a data distribution, which then tails off to the right, the distribution is referred to as
A. rightward skewed.
B. normal.
C. uniform.
D. leftward skewed.
28. To answer the question, refer to the following list of raw data.
63, 71, 72, 77, 77, 78, 86, 77, 88, 88
What is the mode for the data?
A. 88
B. 77.5
C. 77
D. 77.7
29. Use the following data sample to answer the question.
4, 14, 6, 9, 21, 3, 7, 10
What is the variance of this data sample?
A. 34.79
B. 243.5
C. 4.31
D. 5.90
30. Which of the following involves inferential statistics as opposed to descriptive statistics?
A. The Alcohol, Tobacco and Firearms department reported that Houston had 1,791 registered gun dealers in 1997.
B. The city business office reported 35 building permits for new single-family housing units.
C. A local cable system, using a sample of 500 subscribers, estimates that 40 percent of its subscribers watch a premium channel
at least once per day.
D. A class of 50 statistics students earned an average grade of 73.5.
31. Which of the following statements about interpreting standard deviation is true?
A. The Empirical Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. Chebyshev's Rule can
be applied to any data set, regardless of the shape of its frequency distribution.
B. Chebyshev's Rule can't be applied unless the frequency distribution is mound-shaped and symmetric. The Empirical Rule can
be applied to any data set, regardless of the shape of its frequency distribution.
C.Neither Chebyshev's Rule nor the Emprical Rule require any assumptions about the frequency distribution.
D. Neither the Empirical Rule nor Chebyshev's Rule can be applied to data unless the frequency distribution is mound-shaped
and symmetrical.
32. A population is a collection of _______ about which we will measure certain characteristics or
properties, called _______.
A. experimental units, variables
B. individuals, sample values
C. people, traits
D. data, numbers
33. Which of the following are parameters of a population?
A. α and σ
B. μ and σ
C. σ and n
D. μ and x
34. Consider the following chart:
Which of the measures of central tendency would best represent that data?
A. Median
B. Mode
C. Standard deviation
D. Mean
35. Use the following data sample to answer the question.
4, 14, 6, 9, 21, 3, 7, 10
What is the mean of this data sample?
A. 7
B. 8
C. 9.25
D. There's no mean value.
36. To answer the question, refer to the following data.
Ten students were sampled at random from a student population. Each was asked how many courses he or
she was planning on studying in the upcoming year. The following is a list of the reported data values: 1, 2,
2, 3, 4, 5, 5, 5, 5, 6
What is the standard deviation for the data values?
A. 1.44
B. 2.84
C. 2.56
D. 1.687
37. In a sample with mean x = 12 and standard deviation s = 3.5, a data point at 16.8 would have what
samplez-score?
A. 1.37
B. 1.4
C. 4.8
D. We can't know the answer without knowing the population meanμ and standard deviation σ.
38. When creating a histogram, it's important to ensure that the classes of data satisfy which properties?
A. They must be mutually exclusive and exhaustive.
B. They must include each interval on the number line.
C. No requirements are made; the individual creating the graph is free to choose any classes.
D. They must be all the same size.
39. What is the difference between a histogram and a bar chart?
A. The adjacent rectangles in a histogram have a gap, while those for a bar chart don't.
B. The adjacent rectangles in a bar chart have a gap, while those for a histogram don't.
C. A histogram and a bar chart both reflect qualitative data.
D. A histogram reflects qualitative data, while the bar chart represents quantitative data.
40. When obtaining data by _______ it'smost important to inquire about the purposes of the original
experimenter.
A. collecting data observationally
B. conducting a survey
C. reading a published source
D. performing a designed experiment