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Introductory Statistics Practice Quiz

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Updated on Oct 5, 2011

Introductory Statistics Practice Quiz

Before you begin a statistics course, you may want to get an idea of what you know and what you need to learn. The test will answer some of these questions for you. The test consists of 50 multiple-choice questions covering the topics in this book. Although 50 questions can't cover every concept, skill, or shortcut taught in this book, your performance on the test will give you a good indication of your strengths and weaknesses. Keep in mind, the test does not test all the skills taught in this statistics book.

If you score high on the test, you have a good foundation and should be able to work your way through the book quickly. If you score low on the test, don't despair. This book will take you through the statistics concepts step by step. If you get a low score, you may need to take more than 20 minutes a day to work through a lesson. However, this is a self-paced program, so you can spend as much time on a lesson as you need. You decide when you fully comprehend the lesson and are ready to go on to the next one.

Take as much time as you need to do the test. You will find that the level of difficulty increases as you work your way through the test.

Quiz

  1. The time it takes an employee to drive to work is the variable of interest. What type of variable is being observed?

    a. categorical variable

    b. continuous variable

    c. discrete variable

    d. explanatory variable

  2. A study was conducted to compare two different approaches to preparing for an exam. Twenty high school students taking chemistry volunteered to participate. Ten were randomly assigned to use the first approach; the other ten used the second approach. Each one's performance on the next chemistry exam was recorded. What type of study is this?

    a. experiment with a broad scope of inference

    b. experiment with a narrow scope of inference

    c. sample survey

    d. observational study

  3. Random digit dialing was used to select households in a particular state. An adult in each household contacted was asked whether the household had adequate health insurance. A critic of the poll said that the results were biased because households without telephones were not included in the survey. As a consequence, the estimated percentage of households that had adequate health insurance was biased upward. What type of bias was the critic concerned bout?

    a. measurement bias

    b. nonresponse bias

    c. response bias

    d. selection bias

  4. A study was conducted to determine whether a newly developed rose smelled better than the rose of the standard variety. Twenty students were randomly selected from a large high school to participate in a "smell study." Each selected student smelled both roses in a random order and selected the one that smelled best. What is the population of interest and what are the response and explanatory variables?

    a. The population is all students at the large high school; the response variable is the rose choice; and the explanatory variable is the type of rose.

    b. The population is all students at the large high school; the response variable is the type of rose; and the explanatory variable is the rose choice.

    c. The population is all roses of these two types; the response variable is the rose choice; and the explanatory variable is the type of rose.

    d. The population is all roses of these two types; the response variable is the type of rose; and the explanatory variable is the rose choice.

For problems 5 and 6, consider the following 12 data points: 10, 12, 10, 18, 16, 15, 9, 14, 11, 13, 12, and 16.

  1. What is the median of these data?

    a. 9

    b. 12

    c. 12.5

    d. 13

  2. What is the interquartile range of these data?

    a. 4

    b. 5

    c. 6

    d. 9

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

    a. the range

    b. the interquartile range

    c. the median

    d. the mean

  4. How does one standardize a random variable?

    a. Add the mean.

    b. Subtract the mean.

    c. Add the mean and divide by the standard deviation.

    d. Subtract the mean and divide by the standard deviation.

For problems 9 and 10, consider this information: On any given day, the probability it will rain is 0.32; the probability the wind will blow is 0.2; and the probability that it will rain and the wind will blow is 0.1.

  1. For a randomly selected day, what is the probability that it will rain or the wind will blow?  

    a. 0.42  

    b. 0.52  

    c. 0.58  

    d. 0.62

  2. For a randomly selected day, what is the probability that it will NOT rain and the wind will NOT blow?  

    a. 0.38  

    b. 0.48  

    c. 0.58  

    d. 0.90

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 used a safety belt whenever driving. This information and the gender of the student was recorded as follows:

  1. What is the probability that a randomly selected student is a male who does not use his seat belt?  

    a.  

    b.  

    c.  

    d.

  2. What is the probability that a randomly selected student is a female given that the person is a seat belt user?  

     

    a.  

    b.  

    c.  

    d.

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

    a. no, because the probability that a randomly chosen student is a female does not equal the probability of female given safety belt use  

    b. no, because the number of females who use a safety belt is not equal to the number of males who use a seat belt  

    c. yes, because the sample was randomly selected  

    d. yes, because both genders do use seat belts more than they do not use seat belts

For problems 14 and 15, consider that 1% of a population has a particular disease. A new test for identifying the disease has been developed. If the person has the disease, the test is positive 94% of the time. If the person does not have the disease, the test is positive 2% of the time.

  1. What is the probability that a randomly selected person from this population tests positive?  

    a. 0.0292  

    b. 0.0094  

    c. 0.096  

    d. 0.96

  2. A person is randomly selected from this population and tested. She tests positive. Which of the following best represents the probability that she has the disease?  

    a. 0.0094  

    b. 0.32  

    c. 0.34  

    d. 0.94

Use the following information for problems 16, 17, and 18. On any given day, the probability that Megan will be late for work is 0.2.Whether or not she is late to work is independent from day to day.

  1. Megan was late to work today. What is the probability that she will NOT be late to work tomorrow?

    a. 0.16  

    b. 0.2  

    c. 0.6  

    d. 0.8

  2. Which of the following is closest to the probability that Megan will be late to work at least one of the five days next week?  

    a. 0.00032  

    b. 0.33  

    c. 0.41  

    d. 0.67

  3. What is the probability that Megan will be on time exactly three days and then be late on the fourth one?  

    a. 0.0064  

    b. 0.1024  

    c. 0.16  

    d. 0.512

  4. A train is scheduled to leave the station at 3 P.M. However, it is equally likely to actually leave the station any time from 2:55 to 3:15 P.M. What is the probability it will depart the station early?

      a. 0.25  

    b. 0.33  

    c. 0.67  

    d. 0.75

  5. Let z be a standard normal random variable. Find the probability that a randomly selected value of z is between –2.1 and 0.4.  

    a. 0.1079  

    b. 0.3446  

    c. 0.5475  

    d. 0.6554

  6. Let z be a standard normal random variable. Find z* such that the probability that a randomly selected value of z is greater 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 20 and standard deviation 5.What is the probability that a randomly selected value of X is between 15 and 25?  

    a. 0.32  

    b. 0.68  

    c. 0.95  

    d. 0.997

  8. A random sample of size 25 is selected from a population that is normally distributed with a mean of 15 and a standard deviation of 4.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 15 and a standard deviation of 0.16  

    c. normal with a mean of 15 and a standard of 0.8  

    d. normal with a mean of 15 and a standard deviation of 4

  9. Find t* such that the probability that a randomly selected observation from a t-distribution with 16 degrees of freedom is less than t* is 0.1.  

    a. –1.746  

    b. –1.337  

    c. 1.337  

    d. 1.746

  10. A researcher decides to study the bite strength of alligators. She believes that if she takes a large enough random sample, she will be able to say that the average of the bite strengths she records will be close to the mean bite strength of all the alligators in the population she is studying. Is she 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 favored having the current mayor of a large city run for a second term. The results were that 52% of the registered voters polled were in favor of the second term with a margin or error of 0.04.What does this mean?  

    a. There is only a 4% chance that 52% of the registered voters do not favor the mayor running for a second term.  

    b. The estimated percentage of 52% is sure to be within 4% of the true percentage favoring the mayor's run for a second term.  

    c. With 95% confidence, the estimated percentage of 52% is within 4% of the true percentage favoring the mayor's run for a second term.  

    d. With 96% confidence, the estimated percentage of 52% is equal to the true percentage favoring the mayor's run for a second term.

  12. A national organization wanted to estimate the proportion of adults in the nation who could read at the eighth grade level or higher. The organization decided that it would be nice to have estimates for each state as well. To accomplish this, they took a random sample of adults within each state and combined the data to obtain a national estimate. 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 studying greenbugs on oats. To obtain an estimate of the population in a large oat field, he picked a random point in the field and a random direction. He went to the random starting point and counted the number of greenbugs on the oat plant closest to that point. He then took ten steps in the direction that had been selected at random and counted the number of greenbugs on the closest oat plant. He repeated the process of taking ten steps in the same direction and counting the number of greenbugs on the closest oat plant until he had counted the number of greenbugs on 50 plants. What type of sampling plan is this?  

    a. cluster sampling  

    b. simple random sampling  

    c. stratified random sampling  

    d. systematic random sampling

  14. A researcher set a 95% confidence interval on the mean length of fish in a recreational lake and found it to be from 6.2 to 8.7 inches. Which of the following is a proper interpretation of this interval?  

    a. Of the fish in the recreational lake, 95% are between 6.2 and 8.7 inches long.  

    b. We are 95% confident that the sample mean length of fish in the recreational lake is between 6.2 and 8.7 inches.  

    c. We are 95% confident that the population mean length of fish in the recreational lake is between 6.2 and 8.7 inches.  

    d. There is a 95% chance that a randomly selected fish from the recreational lake will be between 6.2 and 8.7 inches.

  15. A large university wanted to know whether toilet paper in the campus restrooms should be hung so that the sheets rolled off over the top or under the bottom of the roll. Two hundred students were randomly selected to participate in a survey. Each selected student was asked his or her preference on how to hang the toilet paper. Researchers found 66% preferred that the sheets roll over the top of the roll. Which of the following would be used to set a 95% confidence interval on the proportion of this university's student population favoring the sheets to roll off the top?  

    a. 0.66 ± 1.645  

    b. 0.66 ± 1.96  

    c. 0.66 ± 1.96  

    d. 0.66 ± 1.645

  16. An owner of a swimming pool wants to know whether or not she needs to add chlorine to the water. Because of costs and the fact that too much chlorine is unpleasant for swimmers, she wants to be sure that chlorine is needed before adding it. What is the swimming pool owner's null hypothesis and what would be a type I error?  

    a. H0: No additional chlorine is needed in the pool. Type I error would occur if she added chlorine when it was not needed.  

    b. H0: No additional chlorine is needed in the pool. Type I error would occur if she did not add chlorine when it was needed.  

    c. H0: Additional chlorine is needed in the pool. Type I error would occur if she added chlorine when it was not needed.  

    d. H0: Additional chlorine is needed in the pool. Type I error would occur if she did not add chlorine when it was needed.

  17. A consumer advocate group doubted the claim of a candy company that 30% of the packages had a price. They believed the percentage of packages with prizes was much less. Let p be the true proportion of this candy maker's packages that have a prize, and let be the sample proportion of those packages with a prize. What is the appropriate set of hypotheses for the consumer advocate group to test?  

    a. H0: p = 0.3; Ha: p < 0.3  

    b. H0: p = 0.3; Ha: p ≠ 0.3  

    c. H0: = 0.3; Ha: < 0.3  

    d. H0: = 0.3; Ha: ≠ 0.3

  18. Nationally, the percentage of people aged 12 to 54 with myopia (near sightedness) has been reported to be 25%. A researcher believes that a higher percentage of people in the same age group is myopic in her area. To test this assumption, she selects a random sample of people in the region and determines whether each person is myopic. Of 200 people surveyed, 56 are myopic. What is the appropriate test statistic to test the researcher's hypothesis?  

    a. zT =

     

    b. zT =  
  19. c. zT =  

    d. zT =

  20. A statistician was testing the following set of hypotheses: H0: p = 0.86 versus Ha: p ≠ 0.86. Using a random sample of size 178, he found zT = 1.58. What is the p-value associated with this test?  

    a. 0.0285  

    b. 0.0571  

    c. 0.1142  

    d. 0.9429

  21. A statistician conducted a hypothesis test and found the p-value to be 0.04. Using a 5% 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. A forester wanted to determine the mean height of trees in an area that was planted with trees a number of years ago. He selected 36 trees at random and determined the height of each. The sample mean was 54.2 meters, and the sample standard deviation was 8.1 meters.

  1. What is the appropriate multiplier to use in setting a 95% confidence interval on the mean height of trees in the study region?  

    a. 1.690  

    b. 1.96  

    c. 2.028  

    d. 2.030

  2. Given the proper multiplier, which of the following represents a 95% confidence interval on the mean height of trees in this area?  

    a. 54.2 ± multiplier × 8.1  

    b. 54.2 ± multiplier ×  

    c. 54.2 ± multiplier ×  

    d. 54.2 ± multiplier ×

  3. A lightbulb manufacturer wanted to be sure that her bulbs burned, on average, longer than the 1,500 hours advertised. She selected a random sample of 56 bulbs and measured the time it took for each to burn out. The sample mean was 1,512 hours, and the sample standard deviation was 38 hours. What is the appropriate test statistic to test the hypothesis that the manufacturer is interested in?  

    a. tT =  

    b. tT =  

    c. tT =  

    d. tT =

  4. A statistician conducts a test of the following set of hypotheses: H0: μ = 18 versus Ha: μ ≠ 18. Based on a random sample of 42, she found the value of the test statistic to be 1.78.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 = 0.0375

  5. A botanist believes that he has developed a new variety of rose that, on average, has more blooms on each plant than the standard variety for the area. He randomly selects 32 plants from his new variety and 32 plants from the standard variety. The plants are each properly cared for throughout the growing season and the total number of blooms each produces is recorded. 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, 32 observations were taken under the first treatment, and 36 were taken under the second treatment. The sample variance under the first treatment was 6.7 and under the second was 5.9. 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 two-group design. Fifty-four units received the first treatment, and 47 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 3.4 and under the second is 16.7.

  1. What is the standard error of the estimated difference in treatment means (12)?  

     

    a.  

    b.  

    c.  

    d.

  2. Approximately how many degrees of freedom are associated with the standardized estimate of the difference in treatment means (12)?  

    a. 54 + 47 – 2 = 99  

    b. 54 + 47 = 101  

    c.  

    d.

Use the following information for problems 44, 45, and 46. A study has been conducted using a matchedpairs design. Forty pairs were used in the study. The sample standard deviation under the first treatment is 6.5, and the sample standard deviation under the second treatment is 8.6. The standard deviation of the differences within each pair is 12.2.

  1. What is the standard error of the estimated difference in treatment means (12)?  

    a.  

    b.  

    c.  

    d.

  2. How many degrees of freedom are associated with the standardized estimate of the difference in treatment mean (12)?  

    a. 40 – 1 = 39  

    b. 40 + 40 – 2 = 78  

    c. 40  

    d.

  3. A chi-squared goodness-of-fit test was conducted. There were seven categories, but no parameters were estimated. The value of the test statistic was 9.6.What is the p-value associated with the test?  

    a. 0.05 < p < 0.075  

    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 high school counselor wanted to know whether there is a relationship between a student's work outside of school and his or her participation in band. He selected a random sample of 75 students. Each selected student was asked whether he or she worked full or part time during the school year and whether he or she participated in band. The results are in the following table.

  1. What type of test is to be conducted?  

    a. paired t-test  

    b. chi-squared goodness-of-fit test  

    c. chi-squared test of homogeneity  

    d. 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 for the final two problems. A homemaker wanted to know which of two furniture polishes worked best. One week, he decided to use one of the furniture polishes on half of each piece of furniture and to use the other furniture polish on the other half. To decide which half got the first furniture polish, he flipped a coin. A head indicated that the first furniture polish went on the left side; a tail indicated that the first furniture polish went on the right side. Thirty-three pieces of furniture were treated in this fashion. At the end of the week, he asked a friend to rate the appearance of each side on a scale of 1 to 10. This was repeated for all pieces of furniture.

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

    a. z-test  

    b. paired t-test  

    c. independent t-test  

    d. chi-squared test of independence

  2. The first furniture polish scored higher, on average, than the second furniture polish. The value of the test statistic was 1.9. What is the p-value of the test, and what decision would one make concerning the hypotheses using a 5% significance level?  

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