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mathematics
introduction to business statistics
Introduction To Statistical Investigations 1st Edition Beth L.Chance, George W.Cobb, Allan J.Rossman Nathan Tintle, Todd Swanson Soma Roy - Solutions
Scientists gathered data to test the research hypothesis that bees are more likely to sting a target that has already been stung by other bees. On eight separate occasions,they offered a pair of targets to a hive of angry bees; one target in each pair had been previously stung, the other was
Researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, they located seven pairs of identical twins with one member of each twin living in the country, the other in a city.
Refer to Exercises 1.4.8 to 1.4.12. Dr. Arbuthnot€™s actual analysis was different from the analysis you saw earlier. Instead of using each individual birth as a coin toss, Arbuthnot used a sign test with each of the 82 years as a coin toss, and a year with more male births counted as a
a. Based on the study’s result, what is the standardized statistic for this test?b. Strength of evidence: What are your conclusions based on the p-value you found in part (d) from the previous exercise? Are the conclusions the same if you base them off the standardized-statistic you found in
For the “leaning” version of the study from the previous question:a. Statistic: How many times did Krieger choose the correct object? Out of how many attempts? Thus, what proportion of the time did Krieger choose the correct object?b. Simulate: Using an applet, simulate 1,000 repetitions of
In another part of the study, instead of looking at the object, the experimenter kept her eyes on the dog and leaned toward the object. For this part of the study, Krieger got 9 right out of 10.a. Identify the parameter of interest for this part of the study and assign a symbol to it.b. If Krieger
Suppose that we repeated the same study with Krieger, and this time he chose the correct object 12 out of 20 times.a. Conjecture how, if at all, the p-value would change from that reported in Exercise 1.4.19, part (c) (one-sided alternative). Increase Stay the same Decreaseb. Using an applet, fi nd
a. Suppose that you decide to use a two-sided alternative hypothesis. What additional values for the parameter will now be part of the alternative?b. Conjecture how, if at all, the p-value for the two-sided alternative will change compared to that reported in Exercise 1.4.19, part (c) for the
a. Statistic: How many times did Krieger choose the correct object? Out of how many attempts? Th us, what proportion of the time did Krieger choose the correct object?b. Simulate: Using an applet, simulate 1,000 repetitions of having the dog choose between the two objects if he is doing so
a. Identify the parameter of interest for this study and assign a symbol to it.b. If Krieger is just randomly choosing between the two objects, what is the chance that he will choose the correct object?c. State your null hypothesis and an appropriate one-sided alternative hypothesis. Can
Suppose that instead of the actual result (9 right out of 10) Harley had only been right 8 times out of 10.a. Which of the three influences on strength (distance, sample size, one- or two-sided) would change? Which would stay the same?b. Overall, the evidence against the null hypothesis would be
Harley got 9 right out of 10. Suppose instead the numbers had been 18 right out of 20.a. Which of the three influences on strength of evidence (distance, sample size, one- or two-sided) would change? Which would stay the same?b. Overall, the evidence against the null hypothesis would be _______
Just for the sake of this exercise, imagine that the investigators wanted their statistical test to include the possibility that Buzz was a very sadistic dolphin, so malicious that he would willingly give up his own chance at a fish just to deprive Doris.a. How would this thinking affect the
In the actual experiment, Buzz got 15 right out of 16. Suppose he had only guessed right 14 times out of 16.a. Which of the three influences on strength (distance, sample size, one- or two-sided) would change? Which would stay the same?b. Overall, the evidence against the null hypothesis would be
Buzz got 15 right out of 16. Suppose the numbers had been exactly double that: 30 right out of 32.a. Which of the three infl uences on strength of evidence (distance, sample size, one- or two-sided) would change? Which would stay the same?b. Overall, the evidence against the null hypothesis would
Summary. For the analysis based on the data above:a. The distance between p̂ and π is ______ (tiny, small, large, huge).b. The sample size is ______ (tiny, small, large, huge).c. Th alternative hypothesis is _________-sided (one, two).Dr. John Arbuthnot
Suppose (against all historical evidence) Arbuth not had been an early feminist, equally willing to accept an excess of female births as evidence of “Divine Providence.” In that case, his p-value would have been ________ (half, twice) as large.
Based solely on the sample size n (ignoring the value of distance p̂ − π), would you expect the evidence against the null hypothesis to be strong or weak? Explain your reasoning.
Based solely on the observed value of p̂ and the null value for π, would you expect the evidence against the null hypothesis to be strong or weak? Explain your reasoning.
Hypotheses.a. What was Dr. Arbuthnot€™s research hypothesis?b. Let Ï€ be Arbuthnot€™s parameter. Tell in words what Ï€ refers to.c. State in words, and then in symbols, what Dr. Arbuthnot€™s null hypothesis was.d. Was Arbuthnot€™s
Look back to Exercise 1.1.8. Recall that in the last 20 games of Minesweeper she played, the author won 12.a. What if she had played 20 games and won 18? Would that provide stronger, weaker, or evidence of similar strength compared to 12 wins out of 20, to conclude that her long run proportion of
Identify these statements as either true or false.a. Using a simulation-based test, the p-value for a two-sided test will be about twice as large as the corresponding p-value for a one-sided test.b. We run tests of significance to determine if p̂ is larger, smaller, or different than some value.
Suppose you are testing the hypothesis H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.54 and find that your p-value is 0.08. Now suppose you redid your study with each of the following changes. Will your new p-value be larger or smaller than the 0.08 your first obtained?a.
One-sided or two?a. Suppose you want to see if competitors wearing red win more than 50% of the matches in the long run, so you test H0: π = 0.50 versus Ha: π > 0.50. What is your p-value based on the above null distribution?b. Suppose you now want to see if competitors wearing either red or
Which of the following will always be true about the p-value for the racquet-spinning study?A. The p-value increases as the sample proportion that land “up” increases.B. The p-value decreases as the sample proportion that land “up” increases.C. The p-value increases as the sample proportion
Which of the following will always be true about the standardized statistic for the racquet-spinning study?A. The standardized statistic increases as the sample proportion that land “up” increases.B. The standardized statistic decreases as the sample proportion that land “up” increases.C.
Does this racquet-spinning study call for a one-sided or a two-sided alternative?A. One-sided, because there is only one variable: how the label landsB. Two-sided, because there are two possible outcomes: up or downC. One-sided, because the researchers want to know whether the label is more likely
Suppose that you wanted to investigate whether people tend to pick a “big” number (3 or 4) rather than a “small” number (1 or 2).a. Based on the value of the standardized statistic obtained in the previous question, do you anticipate the p-value to be small? Why or why not?b. Use an
Suppose that you wanted to investigate whether people tend to pick a “big” number (3 or 4) rather than a “small” number (1 or 2).a. In this context, define the parameter of interest and assign a symbol to it.b. State the null hypothesis and the alternative hypothesis using the symbol defi
a. Based on the value of the standardized statistic obtained in the previous question, do you anticipate the p-value to be small? Why or why not?b. Use an appropriate applet to fi nd and report the p-value. Also, interpret the p-value. (Hint: Th e p-value is the probability of … assuming. …)c.
a. Define the parameter of interest in the context of the study and assign a symbol to it.b. State the null hypothesis and the alternative hypothesis using the symbol defi ned in part (a).c. What is the observed proportion of times students chose the number 3? What symbol should you use to
a. Based on the value of the standardized statistic obtained in the previous question, do you anticipate the p-value to be small? Why or why not?b. Use an appropriate applet to fi nd and report the p-value. Also, interpret the p-value. (Hint: Th e p-value is the probability of … assuming. …)c.
a. Define the parameter of interest in the context of the study and assign a symbol to it.b. State the null hypothesis and the alternative hypothesis using the symbol defined in part (a).c. What is the observed proportion of times the infants picked the helper toy? What symbol should you use to
In a related study, Zwerg, when given two choices, successfully chose the object indicated by a “marker” 26 out of 48 times. Does this result show that Zwerg can correctly follow this type of direction (“placing a marker”) by an experimenter more than 50% of the time?a. Define the parameter
In one study, Zwerg, when given two choices, successfully chose the object pointed at by the experimenter 37 times out of 48 trials. Does this result show that Zwerg can correctly follow this type of direction (“pointing at”) by an experimenter more than 50% of the time?a. Define the parameter
For this study:a. Define the parameter of interest in the context of the study and assign a symbol to it.b. State the null hypothesis and the alternative hypothesis using the symbol defined in part (a).c. What is the observed proportion of times the lady correctly identified what was poured first
For this study:a. State the null hypothesis and the alternative hypothesis in the context of the study.b. Determine the standardized statistic from the data.c. Interpret the standardized statistic in the context of the study.d. Based on the standardized statistic, state the conclusion that you
A previous exercise (1.2.16) introduced you to a study of 40 heterosexual couples. In 28 of the 40 couples the male said “I love you” first. Th e researchers were interested in learning whether these data provided evidence that in significantly more than 50% of couples the male says “I love
Suppose that instead of H0: π = 0.50 like it was in the previous exercise, our null hypothesis was H0: π = 0.60.a. In the context of this null hypothesis, determine the standardized statistic from the data where 80 of 124 kissing couples leaned their heads right. (Hint: You will need to get the
Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos end to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist Onur Güntürkün conjectured that this
Recall that in the second study mentioned (where they later found out that the fish-delivering equipment had been malfunctioning), out of 28 attempts, Buzz pushed the correct button 16 times. Calculate the standardized statistic for these data to investigate whether Buzz’s results provide
Recall that in the first study, out of 16 attempts, Buzz pushed the correct button 15 times. Calculate the standardized statistic for these data to investigate whether Buzz’s results provide convincing evidence that his long-run proportion of pushing the correct button is higher than 0.50. Report
Recall that one of the authors likes to play the game Minesweeper (Exercise 1.1.8) and in the last 20 games she played she won 12. Use an applet to conduct appropriate simulations in order to calculate the standardized statistic for these data and investigate whether her results provide convincing
Suppose that you play the game, again, with two other friends separately with the following results:Friend F chose rock 15 times out of 40 games.Friend G chose rock 30 times out of 40 games.Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock
Suppose that you play the game, again, with two other friends separately with the following results:Friend D chose rock 200 times out of 400 games.Friend E chose rock 20 times out of 40 games.Suppose that for each friend you want to test whether the long-run proportion that the friend will pick
Suppose that you play the game with three different friends separately with the following results:Friend A chose scissors 100 times out of 400 games.Friend B chose scissors 20 times out of 120 games.Friend C chose scissors 65 times out of 300 games.Suppose that for each friend you want to test
Suppose that a standardized statistic (standardized sample proportion) for a study is calculated to be 2.45. Which of the following is the most appropriate interpretation of this standardized statistic?A. The observed value of the sample proportion is 2.45 SDs away from the hypothesized parameter
Identify these statements as either true or false.a. A p-value can be negative.b. A standardized statistic can be negative.c. We run tests of significance to determine whether p̂ is larger or smaller than some value.d. As a p-value gets smaller, its corresponding standardized statistic gets closer
Suppose that your hypotheses are H0: π = 0.25 and Ha: π < 0.25. In the context of these hypotheses, which of the following standardized statistics would provide the strongest evidence against the null hypothesis and for the alternative hypothesis? Why?A. z = –1B. z = 0C. z = 3D. z = –1.80
Consider the two null distributions (A and B) given below, both for proportion of successes. For which null distribution will the standardized statistic for a sample proportion value of 0.60 be farther from 0? How are you deciding? A. 90 Mean = 0.502 SD = 0.049 60 30 0.32 0.36 0.40 0.44 0.48 0.52
Consider the output given below that was obtained using the One Proportion applet. Use information from the output to find the standardized statistic for a sample proportion value of 0.45. Probability of success (T): 0.30 25 Sample size (n): 1000 Number of samples: Animate Draw Samples Total = 1000
Which standardized statistic (standardized sample proportion) gives you the strongest evidence against the null hypothesis?A. z = 1B. z = 0C. z = –3D. z = 1.80
Suppose you retest your friend from the previous question to see if he is a worse free throw shooter than the NBA average of 75%. He shoots 20 more free throws and again makes 12 of them. You combine the data from the two tests together so he made 24 of his 40 attempts. Based on this, do you have
Suppose your friend says he can shoot free throws as well as someone in the NBA and you don’t think he is that good. You know that the NBA average for shooting free throws is 75% and decide to test your friend. You have him shoot 20 free throws and he makes 12 of them. Based on this, do you have
According to Stanford mathematics and statistics professor Persi Diaconis, the probability a flipped coin that starts out heads up will also land heads up is 0.51. Suppose you want to test this. More specifically, you want to test to determine if the probability that a coin that starts out heads up
It has been stated that spinning a coin on a table will result in it landing heads side up fewer than 50% of the time in the long run. One of the authors tested this by spinning a penny 50 times on a table and it landed heads side up 21 times. A test of significance was then conducted with the
While the author in the previous question likes to play Minesweeper, another author likes to play Spider Solitaire on the computer. In his last 40 games, he won 24 of them. Use an applet to find the p-value to investigate whether his results provide convincing evidence that his long-run proportion
Recall that one of the authors liked to play the game Minesweeper (Exercise 1.1.8) and she won 12 of the last 20 games she played. Now that you know how to calculate p-values, use an applet to find the p-value to investigate whether her results provide convincing evidence that her long-run
In one part of the study, the experimenter approached individual rhesus monkeys and placed two boxes an equal distance from the monkey. The experimenter then placed food in one of the boxes, making sure that the monkey could tell that one of the boxes received food without revealing which one.
a. Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.b. Describe in words the parameter of interest for this study and assign a symbol to it.c. Determine the sample proportion of monkeys who picked the box towards which the human
The researchers also interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said “I love you.” Th e students were asked, “Think about your last or current romantic relationship in which someone confessed
a. Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.b. State the appropriate null and alternative hypotheses (in words) for testing whether males are more likely to say “I love you” first. We can express these hypotheses with
Suppose you determine that in order to evaluate some data you need to conduct a simulation analysis.a. In your own words explain how to conduct a simulation using a six-sided die where the sample size is 20 and the null hypothesis probability is 1/6. Be specific.b. Referring to part (a), explain
Suppose two researchers are conducting studies about animal behavior, and they both have the same null hypothesis and the same alternative hypothesis as each other. Also, suppose that Researcher A’s study results produce a p-value of 0.034, whereas Researcher B’s study results produce a p-value
Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You put Hope through 20 trials and 12 times (or 60%) she goes to the correct object when given a choice between two objects. You then conduct a test of significance and generate the following 100 simulations
A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Th en Sarah was shown two photographs, one that
What is the difference between p̂ and the p-value?
Explain the meaning of each of the following symbols.a. H0b. Hac. p̂d. πe. n
Suppose you are testing the hypotheses H0: π = 0.25 and Ha: π < 0.25 and the observed statistic, p̂ is equal to 0.30 with a sample size of 100.a. If you are using a proportion as your statistic, where do you expect your null distribution to be centered?b. If you are using a count as
When we get a p-value that is very small, we may conclude that:A. The null hypothesis has been proven to be true.B. There is strong evidence for the alternative hypothesis.C. The null hypothesis is plausible.D. The alternative hypothesis has been proven to be false.
When we get a p-value that is very large, we may conclude that:A. The null hypothesis has been proven to be true.B. There is strong evidence for the alternative hypothesis.C. The null hypothesis is plausible.D. The alternative hypothesis has been proven to be false.
When using the coin-flipping chance model, the most important reason you repeat a simulation of the study many times is:A. To see whether the null distribution follows a symmetric, bell-shaped curveB. To see whether the null distribution is centered at 0.50C. To see whether your coin is really
The simulation (flipping coins or using the applet) done to develop the distribution we use to find our p-values assumes which hypothesis is true?A. Null hypothesisB. Alternative hypothesisC. Both hypothesesD. Neither hypothesis
Suppose a researcher is testing to see if a basketball player can make free throws at a rate higher than the NBA average of 75%. Th e player is tested by shooting 10 free throws and makes 8 of them. In conducting the related test of significance we have a computer applet do an appropriate
The p-value of a test of significance is:A. The probability, assuming the null hypothesis is true, that we would get a result at least as extreme as the one that was actually observedB. The probability, assuming the alternative hypothesis is true, that we would get a result at least as extreme as
Th e graph of a null distribution will be centered approximately on:A. The observed proportionB. The observed countC. The value of the probability in the null hypothesisD. The number of repetitions performed
After you conduct a coin-flipping simulation, a graph of the _______ will be centered very close to 0.50. Choose from (A)–(D).A. Process probabilityB. Sample sizeC. Number of headsD. Proportion of heads
If an observed statistic from a study turns out to be a likely value under the chance model, then:a. We can say we have evidence against the chance model.b. We can say that the chance model is plausible.c. We can say that the chance model is true.d. We can’t say anything about the chance model,
Suppose Jerry continues to serve and gets 60 out of 100 serves in. Use the One Proportion applet again to test if Jerry’s long-run proportion of getting his first serve in is greater than 50%. State the values you would enter into the applet.a. Probability of heads _____________b. Number of
What values would you enter into the One Proportion applet to run an analysis for Jerry?a. Probability of heads _____________b. Number of tosses _______________c. Number of repetitions ____________d. Use the applet to conduct the simulation study. If Jerry’s long-run proportion of getting his new
Use the data where Janine serves 17 out of 30 right handed short serves into the court. In order to discern whether or not Janine can serve a majority of her short serves in, we will employ the 3S strategy.a. Statistic: How many times did Janine get a short serve in? Out of how many service
Janine serves 30 short serves with her right hand and gets 17 of the 30 in the court.a. What are two possible explanations for Janine getting 17 out of 30 right-handed short serves in?b. Which of the two explanations in part (a) do you think is more plausible? No need to perform an analysis yet;
In order to discern whether or not Janine can land a majority of her short serves in bounds, we will employ the 3S strategy.a. Statistic: How many times did Janine land a short serve in bounds? Out of how many service attempts?b. Simulate: Using an applet, simulate 1,000 repetitions of having
a. What is the parameter in this scenario?b. What are two possible explanations for Janine getting 23 out of 30 left -handed short serves in bounds?c. Which of the two explanations from part (b) do you think is more plausible? No need to perform an analysis yet; explain your answer using only your
Refer to the data in the previous question where Zwerg successfully chose the object with the marker 26 out of 48 times. In order to discern whether Zwerg is doing better than just guessing (50% correct) we will employ the 3S strategy:a. Statistic: How many times did Zwerg pick the correct object?
In a related study, another experimenter-given cue was to place a marker in front of the correct object. Zwerg successfully chose the object with the marker 26 out of 48 times. Does this result show that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the
In order to discern whether Zwerg is doing better than just guessing (50% correct), we will employ the 3S strategy:a. Statistic: How many times did Zwerg pick the correct object? Out of how many attempts?b. Simulate: Using an applet, simulate 1,000 repetitions of having Zwerg choose between the two
a. What is the parameter of interest for this study?b. What are two possible explanations for Zwerg’s results of choosing the correct object 37 out of 48 times?c. Which explanation of the two suggested in part (b) do you think is the more plausible, based on Zwerg’s results? Explain. Note:
Suppose that I try to discern whether tea or milk is poured first for 8 cups and make the correct identification 5 times.a. I say: “5 out of 8 is more than half, so one must conclude that I’m doing better than random guessing.” How would you respond? Use simulation results in your response.b.
a. Describe how you can use a coin to address the question “Is it unlikely that the woman could get all eight correct if she were randomly guessing with each cup?” Be sure to include details such as how many times you would toss the coin and why; what would “heads” and “tails” stand
a. Identify the observational units and variable in this study.b. Identify the parameter for this study. (Hint: Th e long-run proportion that…)c. Identify the sample size. Also, identify the observed value of the statistic for this study.d. Is it possible that the woman could get all eight
Mark is practicing his tennis serves. He wants to be able to tell newspaper reporters the long-run proportion of getting his fi rst serve in. Mark gets 17 of his first 20 serves in.a. Is 17 out of 20 = 85% a statistic or a parameter?b. Is the long-run proportion of Mark’s first serve being in a
If you drop a piece of buttered toast on the floor, is it just as likely to land buttered side up as buttered side down? It sure seems like mine always lands buttered side down! Suppose that 7 of the last 10 times I dropped toast it landed buttered side down. In order to carry out a statistical
The dotplot generated below by the One Proportion applet assumed the long-run proportion of winning was equal to 50%. Use this dotplot to answer the following questions. a. How many dots are in the dotplot?b. What does each dot represent in terms of Minesweeper games and wins?c. At what number is
One of the authors sometimes likes to play Minesweeper, and of the last 20 times she played Minesweeper, she won 12 times. Th at is, she won 60% of the games.a. Based on these 20 games, we would like to learn about her long-run proportion of winning at Minesweeper. Is this value a parameter or a
If Dwyane Wade of the Miami Heat hits 52 out of his fi rst 100 fi eld goals in the 20132014 season, let’s see how we might investigate if he is more likely than not to make a field goal?a. Based on these first 100 field goals, we want to find out what Dwyane’s long-run proportion of making a
Dwyane Wade of the Miami Heat hit 569 of his 1,093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane’s career, can we say that Dwyane is more likely than not to make a field goal?a. Is the long-run proportion of Dwyane making a field goal
LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 20122013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron’s career, can we say he is more likely than not to make a fi eld goal?a. Describe the parameter of interest.b. Is 56.5% a parameter or a
Which of the following is the most important reason that a simulation analysis would repeat the coin-flipping process many times?A. To see whether the distribution of sample proportions follows a normal, bell-shaped curveB. To see whether the distribution of sample proportions is centered at 0.50C.
To conduct a simulation analysis of this racquet spinning study for either 1.1.1 or 1.1.2, you could flip a coin ____ times and repeat that process _____ times.A. 100, 1,000B. 1,000, 100C. 100, 1D. 1, 1,000Tennis players often spin a racquet to decide who serves first. The spun racquet can land
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