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Statistics Practice Quiz

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Updated on Oct 5, 2011

Statistics Practice Quiz

The test has 50 multiple-choice questions covering the topics you studied in this statistics book. Although the format of the test is similar to that of the introductory test, the questions are different.

Take as much time as you need to complete the test. When you are finished, check your answers with the answer key that follows. Once you know your score on the test, compare the results with the introductory test (Introductory Statistics Practice Test). If you score better on the test than you did on the introductory test, congratulations! You have profited from your hard work. At this point, you should look at the questions you missed, if any. Do you know why you missed the question, or do you need to go back to the lesson and review the concept?

If your score on the test doesn't show much improvement, take a second look at the questions you missed. Did you miss a question because of an error you made? If you can figure out why you missed the problem, then you understand the concept and simply need to concentrate more on accuracy when taking a test. If you missed a question because you did not know how to work the problem, go back to the lesson and spend more time working that type of problem. Take the time to understand basic statistics thoroughly. You need a solid foundation in statistics if you plan to use this information or progress to a higher level of statistics. Whatever your score on this test, keep this book for review and future reference.

Quiz

  1. The number of students eating a meal in the school cafeteria is the variable of interest. What type of variable is being observed?

    a. a categorical variable

    b. a continuous variable

    c. a discrete variable

    d. a explanatory variable

  2. A study was conducted to compare the strength of four paper towel brands. A roll of each of the paper towel brands was purchased in a local store. Ten sheets were taken from each roll and tested for strength. What type of study is this?

    a. an experiment with a broad scope of inference

    b. an experiment with a narrow scope of inference

    c. a sample survey

    d. an observational study

  3. Random-digit dialing was used to select households in a particular state. An adult in each household contacted was asked whether anyone in the household had been imprisoned within the past ten years. A critic of the poll said that the results were biased because people living in households where someone has been imprisoned in the past ten years might be embarrassed and respond no. As a consequence, the estimated percentage of households in which someone had been imprisoned in the past ten years would be biased downward. What type of bias was the critic concerned about?

    a. a measurement bias

    b. a nonresponse bias

    c. a response bias

    d. a selection bias

  4. A company has a newly developed sugar substitute that is believed to taste better than the sugar substitute it currently makes. To find out if this is correct, 40 students were randomly selected from the students at a nearby large university. Each selected student was asked to taste the two substitutes in random order. A glass of water was drunk between the two tastings to eliminate lingering effects from tasting the first substitute. Each student was asked to identify which sugar substitute tasted better. What is the population of interest and what are the response and explanatory variables?

    a. The population is all students at the large university, the response variable is the identification of the better tasting sugar substitute, and the explanatory variable is the type of sugar substitute.

    b. The population is all students at the large university, the response variable is the type of sugar substitute, and the explanatory variable is the identification of the better tasting sugar substitute.

    c. The population is the two sugar substitutes, the response variable is the identification of the better tasting sugar substitute, and the explanatory variable is the type of sugar substitute.

    d. The population is the two sugar substitutes, the response variable is the type of sugar substitute, and the explanatory variable is the identification of the better tasting sugar substitute.

For problems 5 and 6, consider the following twelve data points: 8, 10, 8, 16, 14, 13, 7, 12, 9, 11, 10, and 14.

  1. What is the median of these data?

    a. 10

    b. 10.5

    c. 11

    d. The median is not unique.

  2. What is the interquartile range of these data?

    a. 4

    b. 5

    c. 6

    d. 9

  3. What does the line in the middle of the box in a boxplot represent?

    a. the first quartile

    b. the median

    c. the third quartile

    d. the mean

  4. A random variable has a mean of 10 and a standard deviation of 5. After standardizing the random variable, what is its mean and variance?

    a. The mean is 0, and the standard deviation is 1.

    b. The mean is 0, and the standard deviation is 5.

    c. The mean is 10, and the standard deviation is 1.

    d. The mean is 10, and the standard deviation is 5.

Use the following information for problems 9 and 10. In a large city, the proportion of households having a dog is 0.4. The proportion of households having a cat is 0.3. The proportion of households having both a dog and a cat is 0.15.

  1. What proportion of households has a dog or a cat?

    a. 0.45

    b. 0.55

    c. 0.70

    d. 0.85

  2. What proportion of households has neither a dog nor a cat?

    a. 0.15

    b. 0.30

    c. 0.45

    d. 0.85

Use the following information for problems 11, 12, and 13. The students in a small high school were surveyed. Each student was asked whether he or she consistently exceeded the speed limit. This information and the gender of the student was recorded as follows:

Posttest  

  1. What is the probability that a randomly selected student is a female who does not consistently exceed the speed limit?

    a.

    b.

    c.

    d.

  2. What is the probability that a randomly selected student is a male, given that the person consistently exceeds the speed limit?

    a.

    b.

    c.

    d.

  3. Is the use of a safety belt independent of gender?

    a. no, because the probability of male does not equal the probability of male, given the student consistently exceeds the speed limit

    b. no, because the number of males who consistently exceed the speed limit is not equal to the number of males who consistently exceed the speed limit

    c. yes, because the sample was randomly selected

    d. yes, because the probability that a randomly selected male consistently exceeds the speed limit is greater than the probability that a randomly selected female consistently speeds

Use the following information for problems 14 and 15: 0.05% of the parts produced in a manufacturing process are defective. Each part is tested for defects. If the part is defective, the test will indicate it is defective 98% of the time. If the part is not defective, the test will indicate it is defective 1% of the time.

  1. What is the probability that a randomly selected part from this population tests defective?

    a. 0.0095

    b. 0.01485

    c. 0.0585

    d. 0.98

  2. A part is randomly selected from this population and tested. It tests defective. Which of the following best represents the probability that the part is defective?

    a. 0.0490

    b. 0.1624

    c. 0.8376

    d. 0.98

Use the following information for problems 16, 17, and 18. A farmer has determined the probability that a hen lays an egg on any given day is 0.9.Whether she lays or not is independent from day to day.

  1. The hen laid an egg today. What is the probability that she will NOT lay an egg tomorrow?

    a. 0.09

    b. 0.1

    c. 0.8

    d. 0.9

  2. Which of the following is closest to the probability that the hen will NOT lay an egg at least one of the next three days?

    a. 0.001

    b. 0.271

    c. 0.729

    d. 0.999

  3. a. 0.00009

    b. 0.06561

    c. 0.09

    d. 0.6561

  4. Ben is due to work at 8 A.M. He is equally likely to get to work any time between 7:50 and 8:05. Which of the following is closest to the probability Ben will be late on a randomly selected day?

    a. 0.25

    b. 0.33

    c. 0.5

    d. 0.67

  5. Let z be a standard normal random variable. Find the probability that a randomly selected value of z is between –1.6 and 1.2.

    a. 0.0548

    b. 0.1151

    c. 0.8301

    d. 0.8849

  6. Let z be a standard normal random variable. Find z* such that the probability that a randomly selected value of z is less than z* is 0.2.

    a. –0.84

    b. 0.4207

    c. 0.5793

    d. 0.84

  7. Let X be a normal random variable with mean 16 and standard deviation 2.What is the probability that a randomly selected value of X is between 12 and 20?

    a. 0.32

    b. 0.68

    c. 0.95

    d. 0.997

  8. A random sample of size 16 is selected from a population that is normally distributed with a mean of 20 and a standard deviation of 8.What is the sampling distribution of the sample mean?

    a. normal with a mean of 0 and a standard deviation of 1

    b. normal with a mean of 20 and a standard of 0.5

    c. normal with a mean of 20 and a standard deviation of 2

    d. normal with a mean of 20 and a standard deviation of 8

  9. Find t* such that the probability that a randomly selected observation from a t-distribution with 12 degrees of freedom is greater than t* is 0.01.

    a. –3.955

    b. –2.681

    c. 2.681

    d. 3.055

  10. A researcher decides to study how much a sparrow eats during a day. He believes that if he takes a large enough sample that he will be able to say that the sample mean amount of food consumed daily by the sparrows he observes is close to the population mean. Is he correct?

    a. no, one can never be sure that the sample mean is close to the population mean

    b. yes, by the Central Limit Theorem, the sample mean will be equal to the population mean if n > 30

    c. yes, by the Central Limit Theorem, the sample mean will be approximately normally distributed, and the mean of the sampling distribution will be the population mean

    d. yes, by the Law of Large Numbers, as the sample size increases, the sample mean will get close to the population mean

  11. A poll was conducted to determine what percentage of the registered voters in a swing state favored the incumbent president in a close race for re-election. The results were that 51% of the registered voters polled were in favor of the second term with a margin of error of 0.03.What does this mean?

    a. There is only a 3% chance that 51% of the registered voters do not favor the incumbent president for re-election.

    b. The estimated percentage of 51% is sure to be within 3% of the true percentage favoring the incumbent president for re-election.

    c. With 95% confidence, the estimated percentage of 51% is within 3% of the true percentage favoring the incumbent president for re-election.

    d. With 97% confidence, the estimated percentage of 51% is equal to the true percentage favoring the incumbent president for re-election.

  12. A blood bank in a large city noticed that the percentages of each blood type from donors seemed to differ from the national averages. Wanting to be sure that they kept adequate supplies for the blood types in their community, they decided to conduct a survey. They randomly selected blocks within the city. A nurse was sent to each selected block and recorded the blood type of each person living in that block. The information from all selected blocks was combined to estimate the percentages of each blood type for the city. What type of sampling plan is this?

    a. cluster sampling

    b. simple random sampling

    c. stratified random sampling

    d. systematic random sampling

  13. A researcher was interested in estimating the percentage of two-income households in a state. To do this, she took a random sample of households within each county and determined whether or not each selected household had two incomes. She then combined the information from the counties to get an estimate for the state. What type of sampling plan is this?

    a. cluster sampling

    b. simple random sampling

    c. stratified random sampling

    d. systematic random sampling

  14. A student set a 90% confidence interval on the mean time it took him to get from his home to the band practice field and found it to be 12.4 to 15.6 minutes. Which of the following is an appropriate interpretation of this interval?

    a. Ninety percent of the time, the student will take between 12.4 and 15.6 minutes to get to the practice field. b. There is a 90% probability that the mean time it takes the student to get to the practice field is between 12.4 and 15.6 minutes.

    c. We are 90% confident that the sample mean time that the student took to get to the practice field is between 12.4 and 15.6 minutes.

    d. We are 90% confident that the mean time that the student takes to get to the practice field is between 12.4 and 15.6 minutes.

  15. A large university wanted to know whether the students would favor a $5 increase in student fees to fund popular bands to give free student concerts on campus. A random sample of 250 students was selected. Each selected student was asked whether he or she favored the increase in student fees for this purpose. Of those sampled, 57% favored the increase. Which of the following would be used to set a 90% confidence interval on the proportion of all students at this university who would favor such an increase?

    a.

    b.

    c.

    d.

  16. A homeowner thinks she may need a new roof. Because of costs, she wants to be sure a new roof is really needed before having the current one replaced. What is the homeowner's null hypothesis and what would be a type I error?

    a. H0: A new roof is not needed. A type I error would occur if she had a new roof put on when it was not needed.

    b. H0: A new roof is not needed. A type I error would occur if she did not have a new roof put on when it was needed.

    c. H0: A new roof is needed. A type I error would occur if she had a new roof put on when it was not needed.

    d. H0: A new roof is needed. A type I error would occur if she did not have a new roof put on when it was needed.

  17. The mean value of homes in a large city was reported to be $157,000. The local chamber of commerce thought the mean value of homes was higher than this reported value. Let μ be the mean value of home in the city, and let be the mean value of homes in a randomly selected sample of homes in the city. What is the appropriate set of hypotheses for the chamber of commerce to test?

    a.

    b.

    c.

    d.

  18. Nationally, the percentage of people with asthma has been reported to be 6%. A researcher believes that a lower percentage than that has asthma in his region. To test this assumption, he selects a random sample of people in the region and determines whether each person has asthma. Of 200 people surveyed, 9 had asthma. What is the appropriate test statistic to test the researcher's hypothesis?

    a.

    b.

    c.

    d.

  19. A statistician was testing the following set of hypotheses: H0: p = 0.1 versus Ha: p ≠ 0.1. Using a random sample of size 230, she found zT = 1.37.What is the p-value associated with this test?

    a. 0.0426

    b. 0.0853

    c. 0.1706

    d. 0.9147

  20. A statistician conducted a hypothesis test and found the p-value to be 0.06. Using a 10% level of significance, what conclusion should she make?

    a. Accept the null hypothesis.

    b. Do not reject the null hypothesis.

    c. Reject the alternative hypothesis.

    d. Reject the null hypothesis.

Use the following information for problems 36 and 37. An ichthyologist (one who studies fish) wanted to determine the average length of great white sharks in a region that he was studying. He randomly selected 31 of them and measured the length of each. The sample mean was 15.2 feet, and the sample standard deviation was 1.9 feet.

  1. What is the appropriate multiplier to use in setting a 90% confidence interval on the mean length of the great white shark in this region?

    a. 1.645

    b. 1.697

    c. 2.040

    d. 2.042

  2. Given the proper multiplier, which of the following represents a 90% confidence interval on the mean height of trees in this area?

    a.

    b.

    c.

    d.

  3. A car manufacturer wanted to be sure that her cars got at least the average 32 miles/gallon advertised. She selected a random sample of 30 cars and determined the miles/gallon for each. The sample mean was 32.5 miles/gallon, and the sample standard deviation was 2.1 miles/gallon. What is the appropriate test statistic to test the hypothesis that the manufacturer is interested in?

    a.

    b.

    c.

    d.

  4. A statistician conducts a test of the following set of hypotheses: H0: μ = 29 versus the alternative μ < 29. Based on a random sample of 38, he found the value of the test statistic to be 1.85. What is the p-value associated with the test?

    a. 0.0125 < p < 0.025

    b. 0.025 < p < 0.05

    c. 0.05 < p < 0.10

    d. p = 0.0322

  5. A botanist believes that she has developed a new fertilizer that promotes growth in flowers better than the standard fertilizer. She randomly assigns half of her flower plants to the new fertilizer and half to the standard one. The plants are each properly cared for throughout the growing season, and the growth of each plant is recorded at the end of the season. Statistically, what does the researcher want to do?

    a. Compare two treatment means using a matched-pairs design.

    b. Compare two treatment means using a two group design.

    c. Compare the means from two populations.

    d. Compare the means of two samples from the same population.

  6. In a two-group design, 37 observations were taken under the first treatment, and 33 were taken under the second treatment. The sample variance under the first treatment was 9.3 and under the second was 9.8. Believing that both of these are estimates of a common variance, the statistician wants to obtain an estimate of this common variance. How should that be done?

    a.

    b.

    c.

    d. cannot be determined because the sample sizes are not the same for the two treatments

Use the following information for problems 42 and 43. A study has been conducted using a matched-pairs design. Thirty pairs were used in the study. The sample standard deviation under the first treatment is 12.7, and the sample standard deviation under the second treatment is 9.3. The standard deviation of the differences within each pair is 18.4.

  1. What is the standard error of the estimated difference in treatment means ?

    a.

    b.

    c.

    d.

  2. How many degrees of freedom are associated with the standardized estimate of the difference in treatment means ?

     

    a. 30 – 1 = 29

    b. 30 + 30 – 2 = 58

    c. 30 + 30 = 60

    d.

Use the following information for problems 44, 45, and 46. A study has been conducted using a two-group design. Forty-eight units received the first treatment, and 57 received the second treatment. Based on theory, the researcher believes that the variances under the two treatments will be different. The sample standard deviation under the first treatment is 28.4 and under the second is 5.3.

  1. What is the standard error of the estimated difference in treatment means ?

    a.

    b.

    c.

    d.

  2. How many degrees of freedom are associated with the standardized estimate of the difference in treatment means ?

    a. 48 + 57 – 2 = 103

    b. 48 + 57 = 105

    c.

    d.

  3. A chi-squared goodness-of-fit test was conducted. There were five categories, but no parameters were estimated. The value of the test statistic was 8.5.What is the p-value associated with the test?

    a. 0.05 < p < 0.010

    b. 0.10 < p < 0.15

    c. 0.15 < p < 0.20

    d. 0.20 < p < 0.30

Use the following information for problems 47 and 48. A researcher wanted to explore whether one gender was more likely than the other to be myopic (nearsighted). She took a random sample of 40 females and a random sample of 40 males from the students at a large university. She determined whether or not each selected individual was myopic. The results are in the following table:

Posttest

  1. What type of test is to be conducted?

    a. a paired t-test

    b. a chi-squared goodness-of-fit test

    c. a chi-squared test of homogeneity

    d. a chi-squared test of independence

  2. How many degrees of freedom are associated with the test?

    a. 1

    b. 2

    c. 3

    d. 4

Use the following information to answer questions 49 and 50: A golf instructor thinks he has a new way of hitting the ball off of a tee that will make the ball go farther, but will not affect the variability in how far the ball is hit. He randomly selects 100 new golfers. He randomly assigns half of them to be taught the new method and half to be taught using the standard method. He does not tell any of them what he is doing. At the end of the month, he records how far each hits a ball off the first tee.

  1. What is the appropriate statistical test for the hypotheses of interest?

    a. the z-test

    b. a paired t-test

    c. an independent t-test

    d. a chi-squared test of homogeneity

  2. The value of the test statistic was 1.85.What is the t-value of the test and, using a 5% significance level, what is the conclusion?

    a. 0.25 < p < 0.05. Do not reject the null hypothesis.

    b. 0.25 < p < 0.05. Reject the null hypothesis.

    c. 0.05 < p < 0.1. Do not reject the null hypothesis.

    d. 0.05 < p < 0.1. Reject the null hypothesis.

Answers

  1. c
  2. d
  3. c
  4. c
  5. c
  6. b
  7. b
  8. a
  9. b
  10. c
  11. b
  12. a
  13. a
  14. c
  15. c
  16. b
  17. c
  18. b
  19. a
  20. c
  21. a
  22. c
  23. c
  24. c
  25. d
  26. c
  27. a
  28. c
  29. d
  30. d
  31. a
  32. b
  33. b
  34. c
  35. d
  36. b
  37. c
  38. c
  39. b
  40. b
  41. d
  42. a
  43. a
  44. d
  45. d
  46. a
  47. c
  48. a
  49. c
  50. b
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