TEST BANK
Introduction to Statistical Investigations,
2nd Edition Nathan Tintle; Beth L. Chance
Chapters 1 - 11, Complete
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,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
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,Chapter 1
Note: TE = Text entry TE-N = Text entry - NumericMa
= Matching MS = Multiple select
MC = Multiple choice TF = True-FalseE
= Easy, M = Medium, H = Hard
CHAPTER 1 LEARNING OBJECTIVES
CLO1-1: Use the chance model to determine whether an observed statistic is unlikely to occur.
CLO1-2: Calculate and interpret a p-value, and state the strength of evidence it provides againstthe null
hypothesis.
CLO1-3: Calculate a standardized statistic for a single proportion and evaluate the strength ofevidence it
provides against a null hypothesis.
CLO1-4: Describe how the distance of the observed statistic from the parameter value specifiedby the null
hypothesis, sample size, and one- vs. two-sided tests affect the strength of evidence against the null
hypothesis.
CLO1-5: Describe how to carry out a theory-based, one-proportion z-test.
Section 1.1: Introduction to Chance Models
LO1.1-1: Recognize the difference between parameters and statistics.
LO1.1-2: Describe how to use coin tossing to simulate outcomes from a chance model of the ran-dom choice
between two events.
LO1.1-3: Use the One Proportion applet to carry out the coin tossing simulation.
LO1.1-4: Identify whether or not study results are statistically significant and whether or not thechance
model is a plausible explanation for the data.
LO1.1-5: Implement the 3S strategy: find a statistic, simulate results from a chance model, and comment on
strength of evidence against observed study results happening by chance alone.
LO1.1-6: Differentiate between saying the chance model is plausible and the chance model is the correct
explanation for the observed data.
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,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 wearerwins
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. 0.50
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 wearerwins
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. 0.50
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 by chance
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 convincing evidence against the ―by-chance-alone‖ 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 appropriatesimulation
of this process, if Hope does not understand pointing towards an object and isjust 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 = A. 0.5, probability of Hope going to the
Heads = correct object
Tails = B. Hope going to the correct object
Chance of heads = C. Hope going to the incorrect object
One repetition = 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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,1-4 Test Bank for Introduction to Statistical Investigations, 2nd Edition
7. Given below is the resulting simulation distribution from the One Proportion applet. Basedon this
simulation, do we have convincing evidence against the observed study results happening by chance
alone?
A. No, since 0.65 is a fairly typical outcome if Hope was just guessing.
B. No, since we could have observed a value greater than 0.65 just by randomchance.
C. Yes, since 0.65 is larger than 0.5.
D. Yes, since the height of the dotplot above 0.65 is smaller than the height of thedotplot
above 0.5.
Ans: A; LO: 1.1-5; Difficulty: Medium; Type: MC
8. Which of the following is NOT a step in the 3S Strategy for measuring strength ofevidence?
A. Strength of evidence
B. Statistic
C. Sample
D. Simulate
Ans: C; LO: 1.1-5; Difficulty: Easy; Type: MC
Questions 9 through 12:
True or False?
9. A parameter is a number summarizing the results in the sample.
Ans: False; LO: 1.1-1; Difficulty: Easy; Type: TF
10. A result that is unlikely to occur just by chance alone is called statistically significant.
Ans: True; LO: 1.1-4; Difficulty: Easy; Type: TF
11. If an observed statistic is statistically significant, then we have strong evidence that thechance-
alone explanation is correct.
Ans: False; LO: 1.1-5; Difficulty: Medium; Type: TF
12. If an observed statistic is NOT statistically significant, then the chance model is plausible.
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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 onwhether 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.
0.55
B. p̂ 0.55
C. 825
D. p̂ 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 propernotation in
this study?
A. 𝜋 = 0.50
B. 𝑝̂ = 0.50
C. 825
D. p̂ 825
Ans: A; LO: 1.2-1; Difficulty: Easy; Type: MC
15. State the null and alternative hypotheses in proper notation.
A. H0 : 0.50 vs Ha : 0.55
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,1-6 Test Bank for Introduction to Statistical Investigations, 2nd Edition
B. H0 : 0.55 vs Ha : 0.55
C. H0 : 0.50 vs Ha : 0.50
D. H0 : p̂ 0.50 vs Ha : p̂ 0.50
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. 0.55
B. 0.50
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 theproblem.
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 participatein 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 ofYellowstone National
Park entered their den for hibernation by the last day of November. This
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has come into question as of late. Researchers have hypothesized that climate change has postponed bears
entering hibernation until later in the season; that is, researchers believe that a smaller percentage of bears are
entering their den for hibernation by the last day of November. Sixty-two Yellowstone grizzly bears were
tracked via radio monitors, which allow scientists to pinpoint when the bears enter their dens with a high
degree of accuracy. Of the sixty-two Yellowstone grizzly bears being tracked, forty-two entered their den for
hibernation by the last dayof November.
19. Identify which of the following is the null hypothesis, and which is the alternative
hypothesis:
The sample proportion of 62 Yellowstone grizzly bears that enter their den for
hibernation by the last day of November is 0.80.
The long-run proportion of Yellowstone grizzly bears that enter their den for
hibernation by the last day of November is 0.80.
The long-run proportion of Yellowstone grizzly bears that enter their den for
hibernation by the last day of November is less than 0.80.
_ The long-run proportion of Yellowstone grizzly bears that enter their den for
hibernation by the last day of November is greater than 0.80.
Ans: 2nd blank = Null; 3rd blank = Alternative; LO: 1.2-2; Difficulty: Medium; Type: MC
20. What values would you enter for each of the following in the One Proportion applet toconduct a
simulation-based hypothesis test with these data?
Probability of success: Sample
size:
Number of samples:
Ans: 0.8 (Tol: 0), 62 (Tol: 0), Any integer as larger or larger than 1000; LO: 1.2-4;Difficulty: Easy;
Type: TE-N
21. A distribution of simulated ―Number of successes,‖ assuming the null hypothesis is true, isshown
below. Circle the portion of the plot below that you would count to calculate the p- value.
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