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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

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
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)
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?
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
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)
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)
Summary. For the analysis based on the data above:a. The distance between pÌ‚ and Ï€ is ______ (tiny, small, large, huge).b. The sample size is ______ (tiny, small, large,
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
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
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
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.
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
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
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
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”
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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.
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
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
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
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
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%.
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 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
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
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
a. Suppose that the spun racquet lands with the label facing up 24 times out of 100. Explain, as if to a friend who has not studied statistics, why this result does constitute strong evidence against
a. Describe the relevant long-run proportion of interest in words.b. What statistical term is given to the long-run proportion you described in (a)?c. What value does the chance model assert for the
Reload the two mean charts and repeat Applet Exercises 1 through 4. In what way(s) were the results similar and in what way(s) were they different the second time around?
Continuing with the second applet, press the “New Sample” button 65 more times to reach the limit of 100 consecutive samples. Describe the condition of the process during these last 65 samples.
Using the second applet, press the “New Sample” button 35 times. You have now generated 35 samples from the process and the means are shown on the chart. Does the process appear to be in control?
Continuing with the first applet, press the “New Sample” button 90 more times to reach the limit of 100 consecutive samples. Does it appear that the process was in control during the 100 samples?
Using the first applet, press the “New Sample” button 10 times. You have now generated 10 samples from the process and the means are shown on the chart. Does the process appear to be in control?
During the production of 15-ampere circuit breakers, samples are taken at periodic intervals and tested for the exact amperage at which they break a circuit. Each sample consists of n = 4 circuit
An adhesives manufacturer periodically selects a sample of its product and glues 6 toothpicks together, in pairs. A measurement is then made of the number of pounds required to separate the

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