Statistical Investigations Test Bank: Chapter Questions and Answers, Exams of Statistics

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TEST BANK

Introduction to Statistical Investigations,

nd

Edition Nathan Tintle; Beth L. Chance

Chapters 1 - 11, Complete

TABLE OF CONTENTS

Chapter 1 – Significance: How Strong is the Evidence

Chapter 2 – Generalization: How Broadly Do the Results

Apply?

Chapter 3 – Estimation: How Large is the Effect?

Chapter 4 – Causation: Can We Say What Caused the

Effect?

Chapter 5 – Comparing Two Proportions

Chapter 6 – Comparing Two Means

Chapter 7 – Paired Data: One Quantitative Variable

Chapter 8 – Comparing More Than Two Proportions

Chapter 9 – Comparing More Than Two Means

Chapter 10 – Two Quantitative Variables

Chapter 11 – Modeling Randomness

1-2 Test Bank for Introduction to Statistical Investigations , 2nd Edition

Questions 1 through 4:

Do red uniform wearers tend to win more often than those wearing blue uniforms in Taekwondo matches where competitors are randomly assigned to wear either a red or blue uniform? In a sample of 80 Taekwondo matches, there were 45 matches where thered uniform wearer won.

1. What is the parameter of interest for this study? A. The long-run proportion of Taekwondo matches in which the red uniform wearer wins B. The proportion of matches in which the red uniform wearer wins in a sample of 80 Taekwondo matches C. Whether the red uniform wearer wins a match D. 0. Ans: A; LO: 1.1-1; Difficulty: Easy; Type: MC
2. What is the statistic for this study? A. The long-run proportion of Taekwondo matches in which the red uniform wearer wins B. The proportion of matches in which the red uniform wearer wins in a sample of 80 Taekwondo matches C. Whether the red uniform wearer wins a match D. 0. Ans: B; LO: 1.1-1; Difficulty: Easy; Type: MC
3. Given below is the simulated distribution of the number of ―red wins‖ that could happen bychance alone in a sample of 80 matches. Based on this simulation, is our observed result statistically significant?

A. Yes, since 45 is larger than 40. B. Yes, since the height of the dotplot above 45 is smaller than the height of thedotplot above 40. C. No, since 45 is a fairly typical outcome if the color of the winner‘s uniform was determined by chance alone.

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D. No, since we could have observed a value greater than 45 just by random chance. Ans: C; LO: 1.1-4; Difficulty: Medium; Type: MC

4. What can we conclude from the results of this study? Select all that apply. A. The results of this study are something that could easily have happened if thecolor of the winner‘s uniform was determined by chance alone. B. We do not have con vinci ng evi dence aga inst the ―by-chance-a l one‖ model. C. The results of this study prove that the color of the winner‘s uniform was determined by chance alone. D. We do not have convincing evidence that red uniform wearers tend to win moreoften than those wearing blue uniforms. Ans: A, B, D; LO: 1.1-6; Difficulty: Hard; Type: MS

Questions 5 through 8:

Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You place two objects about 2.5 meters away, then you point towards one of the objects. In 20 trials,Hope goes to the correct object 13 times (or 65%).

5. Fill in the blanks with the correct One Proportion applet inputs to carry out an appropriate simulation of this process, if Hope does not understand pointing towards an object and is just guessing. Probability of success: Sample

size: Number of samples: Ans: 0.5 (Tol: 0), 20 (Tol: 0), Any integer as larger or larger than 1000; LO: 1.1-3; Difficulty: Easy; Type: TE-N

6. Match the parts of the real study corresponding to the physical (coin-flipping) simulation: Coin flip = Heads = Tails = Chance of heads = One repetition =

A. 0.5, probability of Hope going to the correct object B. Hope going to the correct object C. Hope going to the incorrect object D. One set of 20 attempts by Hope E. Hope going to an object Ans: E, B, C, A, D; LO: 1.1-2; Difficulty: Medium; Type: Ma

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Ans: True; LO: 1.1-6; Difficulty: Medium; Type: TF

Section 1.2: Measuring Strength of Evidence

LO1.2-1: Use appropriate symbols for parameter and statistic.

LO1.2-2: State the null and the alternative hypotheses in words and in terms of the symbol π, thelong-run proportion.

LO1.2-3: Explain how to conduct a simulation using a null hypothesis probability that is not 50-50.

LO1.2-4: Use the One Proportion applet to obtain the p-value after carrying out an appropriatesimulation.

LO1.2-5: Anticipate the location of the center of the null distribution and how it changes based on whether you are using proportion or count as the statistic.

LO1.2-6: Interpret the p-value.

LO1.2-7: Explain why a smaller p-value provides stronger evidence against the null hypothesis. LO1.2-8:

State a conclusion about the alternative hypothesis and null hypothesis based on the p- value.

Questions 13 through 18:

A survey on 1,500 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a studyabroad program in college. Does this survey provide convincing evidence that the majority (morethan 50%) of all high school seniors who take the SAT are fairly certain they will participate in a study abroad program in college?

13. What is the value of the statistic and its proper notation in this study? A.

B. p ˆ^ 0.

C. 825

D. p ˆ^825

Ans: B; LO: 1.2-1; Difficulty: Easy; Type: MC

14. Under the null hypothesis, what is the value of the parameter of interest and its proper notation in this study?

A. 𝜋 = 0.

B. 𝑝̂ = 0.

C. 825

D. p ˆ^825

Ans: A; LO: 1.2-1; Difficulty: Easy; Type: MC

15. State the null and alternative hypotheses in proper notation. A. H 0 : 0.50 vs Ha : 0.

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B. H 0 : 0.55 vs Ha : 0.

C. H 0 : 0.50 vs Ha : 0.

D. H 0 : p ˆ^ 0.50 vs Ha : p ˆ^ 0.

Ans: C; LO: 1.2-2; Difficulty: Easy; Type: MC

16. Fill in the blanks with the correct values to simulate another survey of 1,500 high school seniors who took the SAT in which the long-run proportion of all high school seniors whotake the SAT that are fairly certain they will participate in a study abroad program in college is 0.50. Create a spinner with percent shaded red, and percent shaded black. Spinthe spinner times. Record the of times the spinner lands on red. Ans: 50 (Tol: 0), 50 (Tol: 0), 1500 (Tol: 0), proportion (or count); LO: 1.2-3; Difficulty: Medium; Type: TE, TE-N
17. Using a count as the statistic, where would you expect the null distribution to be centered?A. 0. B. 0. C. 825 D. 750 Ans: D; LO: 1.2-5; Difficulty: Medium; Type: MC
18. The p-value for this study is less than 0.001. Interpret this value in the context of the problem. A. There is less than a 0.1% chance that 50% of all high school seniors who take theSAT are fairly certain they will participate in a study abroad program in college. B. In less than 0.1% of all samples of 1,500 high school seniors who take the SAT, we would see 55% or more respond that they are fairly certain they will participatein a study abroad program in college, if the true probability is 0.50. C. In less than 0.1% of all samples of 1,500 high school seniors who take the SAT, we would see 50% or more respond that they are fairly certain they will participate in a study abroad program in college, if the true probability is 0.55. D. There is less than a 0.1% chance that more than 50% of all high school seniors who take the SAT are fairly certain they will participate in a study abroad programin college. Ans: B; LO: 1.2-6; Difficulty: Hard; Type: MC

Questions 19 through 23:

Research done in the mid 1980s indicated that 80% of grizzly bears in the greater ecosystem of Yellowstone National Park entered their den for hibernation by the last day of November. This

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Ans:

LO: 1.2-4; Difficulty: Medium; Type: Other

22. How could we use coins, a spinner, or cards to simulate one of the samples in the above simulation? Select all that apply. A. Flip a coin 62 times, where heads represents ―hibernate by November 30.‖ Count the number of heads in 62 flips. B. Create a spinner with 80% shaded to represent ―hibernate by November 30.‖ Spin the spinner 62 times and count the number of times the spinner lands in the shad-ed area. C. Have 8 black cards and 2 red cards where black represents ―hibernate by Novem-

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ber 30‖. Draw with replacement from the cards 62 times and count the number of times a black card is drawn. D. Create a spinner with 68% shaded to represent ―hibernate by November 30.‖ Spin the spinner 62 times and count the number of times the spinner lands in the shad-ed area. Ans: B, C; LO: 1.2-3; Difficulty: Hard; Type: MS

23. The simulation-based p-value for this test is 0.0153. Which of the following conclusions are correct? Select all that apply. A. We have strong evidence against the null hypothesis. B. We have strong evidence in favor of the null hypothesis. C. We have strong evidence against the alternative hypothesis. D. We have strong evidence in favor of the alternative hypothesis. Ans: A, D; LO: 1.2-8; Difficulty: Medium; Type: MS

Questions 24 through 26:

True or False?

24. When using the One Proportion applet, the simulated null distribution should be centeredaround the observed sample proportion. Ans: False; LO: 1.2-5; Difficulty: Easy; Type: TF
25. The p-value is the probability that the null hypothesis is true. Ans: False; LO: 1.2-6; Difficulty: Medium; Type: TF
26. A smaller p-value provides stronger evidence against the null hypothesis. Ans: True; LO: 1.2-7; Difficulty: Easy; Type: TF

Section 1.3: Alternative Measure of Strength of Evidence

LO1.3-1: Find a standardized stat ist ic from the observed proport ion of ―successes,‖ the hypothesized mean, and SD of the null distribution as produced by the One Proportionapplet.

LO1.3-2: Interpret a standardized statistic.

LO1.3-3: State a conclusion about the alternative hypothesis (and null hypothesis) based on the magnitude of the standardized statistic.

LO1.3-4: Recognize that the standardized statistic is an alternative to the p-value.

Questions 27 through 32:

The first iPhone became available for public purchase in 2007. By 2010, approximately 30% ofsmartphone users in the US owned an iPhone. Several new companies have entered the smartphone market since then and the folks at Apple want to know how they are stacking up against their competition. In 2019, a representative sample of 529 smartphone users in the US

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treme, assuming 30% of all US smartphone users use an Apple iOS device, is X. C. The proportion of the US smartphone market that uses an Apple iOS device is X. D. The 0.474 proportion of the US smartphone users sampled who use Apple iOS devices is X standard deviations above the 2010 Apple US market-share of 0.30. Ans: D; LO: 1.3-2; Difficulty: Hard; Type: MC

31. Which of the following strength of evidence statements are correct, based on the stand- ardized statistic in #29? Select all that apply. (If you didn‘t report a standardized statistic in

#29, then use z 4 for this question.)

A. We have very strong evidence against the null hypothesis. B. We have very strong evidence against the alternative hypothesis. C. We have very strong evidence in favor of the null hypothesis. D. We have very strong evidence in favor of the alternative hypothesis. Ans: A, D; LO: 1.3-3; Difficulty: Medium; Type: MS

32. What can we conclude about this study, based on the standardized statistic in #29? (If you

didn‘t report a standardized statistic in #29, then use z 4 for this question.)

A. We have very strong evidence that Apple‘s share of the US smartphone markethas remained the same since 2010. B. We have very strong evidence that Apple‘s share of the US smartphone market has increased since 2010. C. We do not have very strong evidence that Apple‘s share of the US smartphonemarket has increased since 2010. D. We have very strong evidence that the proportion of the representative sample of 529 smartphone users in the US using an Apple iOS device is greater than 0.30. Ans: B; LO: 1.3-3; Difficulty: Medium; Type: MC

33. Match each standardized statistic value with its corresponding p-value: z z 3.

z

A. p-value = 0. B. p-value = 0. C. p-value = 0. Ans: C, A, B; LO: 1.3-4; Difficulty: Medium; Type: Ma

Questions 34 and 35:

Do red uniform wearers tend to win more often than those wearing blue uniforms in Taekwondo matches where competitors are randomly assigned to wear either a red or blue uniform? In a sample of 80 Taekwondo matches, there were 45 matches where the red uniform wearer won. Given below is the simulated null distribution of proportion of ―red wins‖ that could happen by

1 - 12 Test Bank for Introduction to Statistical Investigations , 2nd Edition

chance alone in a sample of 80 matches. Also, given are the mean and SD for this null distribution.

34. What is the value of the standardized statistic? A. z 0. B. z

C. z 1.

D. z

Ans: C; LO: 1.3-1; Difficulty: Easy; Type: MC

35. Is there evidence that in Taekwondo matches, red uniform wearers tend to win more oftenthan those wearing blue uniforms than would be expected by chance alone? A. Yes, since 45 is greater than 30. B. No, since we only observed 80 Taekwondo matches. C. No, since the standardized statistic is between and. 1.5. D. Yes, since the standardized statistic is between and 1.5. Ans: C; LO: 1.3-3; Difficulty: Medium; Type: MC

Questions 36 through 38:

True or False?

36. The standardized statistic represents the number of standard deviations the observed statistic is above or below the hypothesized null value. Ans: True; LO: 1.3-2; Difficulty: Easy; Type: TF
37. If the standardized statistic is larger than 3, then the p-value will be larger than 0.10. Ans: False; LO: 1.3-4; Difficulty: Medium; Type: TF
38. A standardized statistic that is closer to zero provides stronger evidence against the null hypothesis.

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Questions 42 through 51:

An environmental science teacher at a high school with a large population of students was curious whether the majority (more than half) of students at the school regularly recycle plastic bottles. The teacher selected a random sample of 146 students at the school to interview, then asked each student: ―Do you recycle plastic bottles more often than you throw them in the trash?‖ (Yes/No). Suppose that 89 of the students answered ―Yes‖.

42. What is the parameter of interest for this study? A. The proportion of the 146 students in the sample that would answer ―Yes‖ B. The proportion of all students at the school that would answer ―Yes‖ C. All students at the school D. The true mean number of students at the school who would answer ―Yes‖ Ans: B; LO: 1.1-1; Difficulty: Medium; Type: MC
43. What are the null and alternative hypotheses in appropriate notation? A. H 0 : 0.50 vs Ha : 0.

B. H 0 : 0.61 vs Ha : 0.

C. H 0 : 0.50 vs Ha : 0.

D. H 0 : p ˆ^ 0.50 vs Ha : p ˆ^ 0.

Ans: C; LO: 1.2-2; Difficulty: Easy; Type: MC

44. Use the One Proportion applet to calculate a p-value for this study. Ans: 0.005 (Tol = +/- 0.0015); LO: 1.2-4; Difficulty: Hard; Type: TE-N
45. How could we use coins, a spinner, or cards to simulate one of the samples in the simulated null distribution? Select all that apply. A. Flip a coin 146 times, where heads represents ―answered Yes‖. Count the number of heads in 146 flips. B. Create a spinner with 61% shaded to represent ―answered Yes‖. Spin the spinner 146 times and count the number of times the spinner lands in the shaded area. C. Have 5 black cards and 5 red cards where black represents ―answered Yes‖. Draw with replacement from the cards 146 times and count the number of times ablack card is drawn. D. Create a spinner with 50% shaded to represent ―answered Yes‖. Spin the spinner 146 times and count the number of times the spinner lands in the shaded area. Ans: A, C, D; LO: 1.1-2; Difficulty: Easy; Type: MS
46. Would you consider the results of this test to be statistically significant? A. Yes, because the simulated distribution is not centered on the observed statistic. B. No, because the results are unlikely to occur by random chance alone. C. No, because the simulation proves that the null hypothesis is true.

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D. Yes, because the results are unlikely to occur by random chance alone. Ans: D; LO: 1.1-4; Difficulty: Medium; Type: MC

For each of the following ( questions 47 through 51 ), circle whether we would have stronger, weaker, or the same amount of evidence against the null hypothesis, given all other aspects of the study remained the same, or if the answer cannot be determined from the information given

47. The teacher sampled 300 students instead of 146. A. Stronger evidence against the null hypothesis B. Weaker evidence against the null hypothesis C. The same amount of evidence against the null hypothesis D. Cannot be determined from the information given Ans: A; LO: 1.4-4; Difficulty: Medium; Type: MC
48. The sample proportion of students who said ―Yes‖ was 0.75 instead of 0.61. A. Stronger evidence against the null hypothesis B. Weaker evidence against the null hypothesis C. The same amount of evidence against the null hypothesis D. Cannot be determined from the information given Ans: A; LO: 1.4-1; Difficulty: Medium; Type: MC
49. The sample proportion of students who said ―Yes‖ was 0.55 instead of 0.61. A. Stronger evidence against the null hypothesis B. Weaker evidence against the null hypothesis C. The same amount of evidence against the null hypothesis D. Cannot be determined from the information given Ans: B; LO: 1.4-1; Difficulty: Medium; Type: MC
50. We want to know if the proportion of students at the school that would have said ―Yes‖ differed from 0.5 rather than was greater than 0.5. A. Stronger evidence against the null hypothesis B. Weaker evidence against the null hypothesis C. The same amount of evidence against the null hypothesis D. Cannot be determined from the information given Ans: B; LO: 1.4-2; Difficulty: Medium; Type: MC
51. We want to know if less than half of all students at the school would have said ―Yes‖ rather than greater than half. A. Stronger evidence against the null hypothesis B. Weaker evidence against the null hypothesis

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Section 1.5: Inference for a Single Proportion:

Theory-based Approach

LO1.5-1: Predict the shape, mean, and standard deviation of the null distribution of sample pro-portions, as approximately normal (when the sample size is large enough), π, and

√𝜋(1^ −^ 𝜋)/𝑛,^ respectively.

LO1.5-2: Use the One Proportion applet to find the one-proportion z-test (theory-based; normal approximation-based), p-value, and standardized statistic, z.

LO1.5-3: Explain when simulation and theory will yield different answers.

56. The official four-year graduation rate among US colleges and universities is 57.6%. Suppose a researcher takes a random sample of 100 college students and tracks their progress through school to determine whether each student graduates in four years ornot. Which of the following do you know to be true? Select all that apply. A. If many samples of 100 students were taken, the distribution of the sample proportions would be bell-shaped and symmetric. B. If many samples of 100 students were taken, the distribution of the sample proportions would be centered at 0.576. C. The sample proportion collected by the researcher would be 0.576. D. If many samples of 100 students were taken, the standard deviation of the sample proportions would be 0.049. Ans: A, B, D; LO: 1.5-1; Difficulty: Medium; Type: MS

Questions 57 through 63:

A study conducted by the National Center for Health Statistics as part of the Center for Disease Control and Prevention (CDC) found that, as of 2015-2016, 39.6% of Americans over the age of 20 fit the medical definition of being obese (BMI of 30 or higher). A city known for its plentiful outdoor opportunities believes that number is lower among its residents. A representative sampleof 80 city residents is collected and the BMI calculated for each (based on reported height and weight). The variable of interest is whether the resident fit the medical definition of obese. The study found 22 people in the sample fit the medical definition of obese.

57. Is a theory-based method appropriate for these data? A. Yes, because a representative sample was collected. B. Yes, because there were 22 people defined as obese and 58 people not defined as obese in the sample, and both of these values are greater than 10. C. No, because the researcher did not collect a random sample. D. No, because the national obesity rate is not 0.5. Ans: B; LO: 1.5-3; Difficulty: Easy; Type: MC
58. Identify which of the following is the null hypothesis. A. The sample proportion of 80 city residents that fit the medical definition of obese is equal to 0.396.

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B. The long-run proportion of city residents that fit the medical definition of obese isequal to 0.396. C. The long-run proportion of all Americans over the age of 20 that fit the medical definition of obese is equal to 0.396. D. The sample proportion of 80 city residents that fit the medical definition of obese is equal to 0.275. Ans: B; LO: 1.2-2; Difficulty: Medium; Type: MC

59. Identify the correct alternative hypothesis. A. Ha : 0.

B. Ha : 0.

C. Ha : 0.

D. Ha : p ˆ^ 0.

Ans: C; LO: 1.2-2, 1.4-3; Difficulty: Easy; Type: MC

60. Select the appropriate method of calculating the standard deviation of the sample proportions under the null hypothesis.

A.

B.

C.

D.

Ans: A; LO: 1.5-1; Difficulty: Easy; Type: MC

61. Let ‗A‘ represent your answer from #60. Whi ch of the foll owi ng displays the correct method of calculating the standardized statistic?

A. 22 31. 80 A

B.

A

C.

A

D. A^ 0.

Ans: C; LO: 1.5-2; Difficulty: Easy; Type: MC