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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

Th e poll also asked voters to report the amount of time that the respondent spent reading or learning about local politics over the last week. Th e poll finds that, on average, respondents have
Evaluate the strength of evidence for the hypotheses in the previous question.a. Find the p-value for the hypotheses in the previous question using a simulation-based approach.b. Based on the p-value
The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent.a. State the null and alternative hypotheses for this test.b. What
Use the previous information to answer the following questions about the political survey.a. Identify the variable measured on each likely voter.b. Is the variable categorical or quantitative?c.
Use the previous information to answer the following questions about the political survey.a. Describe in words the parameter of interest.b. Identify the numeric value of the statistic corresponding
Use the previous information to answer the following questions.a. What is the population of interest?b. Do you believe that the proportion of likely voters for the incumbent in the sample is likely
Consider how the student obtained her sample for her study. If her study was conducted by taking a random sample, explain (in enough detail that someone could follow your directions to obtain the
Among the students in her class, the information for three particular students is given here:(i) Alejandra reported watching 2 hours of TV a day, but not watching TV yesterday.(ii) Ben reported
Evaluate the strength of evidence for the hypotheses in the previous question.a. Find the p-value for the hypotheses in the previous question using a simulation-based approach.b. Based on the p-value
Using the information from the previous question, the student wishes to test whether there is evidence that more than 50% of students at the school watched at least 10 minutes of TV yesterday.a.
In the survey the student also asked students whether or not they watched at least 10 minutes of TV yesterday. Th e student found that 21 of 30 students reported watching at least 10 minutes of TV
Use the previous information to answer the following questions about the class survey.a. Describe in words the parameter of interest.b. Identify the numeric value of the statistic corresponding to
Use the previous information to answer the following questions about the class survey.a. Identify the variable measured on each student.b. Is the variable categorical or quantitative?c. Identify at
Argue whether or not you believe using a sample of birds which visit a bird feeder in your yard (the next 50 birds that visit) may or may not yield biased estimates based on the variable being
Argue whether or not you believe using a sample of students from your school’s cafeteria (you recruit the next 100 people to visit the cafeteria to participate) may or may not yield biased
When using simulation- or theory-based methods to test hypotheses about a proportion, the process of computing a p-value is:A. Different if the sample is from a process instead of from a finite
When stating null and alternative hypotheses, the hypotheses are:A. Always about the parameter onlyB. Always about the statistic onlyC. Always about both the statistic and the parameterD. Sometimes
True or false?A. Random samples only generate unbiased estimates of long-run proportions, not long-run means.B. Nonrandom samples are always biased.C. Th ere is no way that a sample of 100 people can
True or false?A. Larger samples are always better than smaller samples, regardless of how the sample was collected.B. Larger random samples are always better than smaller random samples.C. You
The reason for taking a random sample instead of a convenience sample is:A. Random samples tend to be smaller and so take less time to collect.B. Random samples tend to represent the population of
In most statistical studies the _______________ is unknown and the ________________ is known.A. Parameter/statisticB. Statistic/parameter
The population will always be _______________ the sample.A. At least as large asB. Smaller than
Do you have strong evidence that the long-run proportion of times a student will choose the right front tire is different than 1/4?
Use a theory-based test to find the p-value. How does this compare with the p-value you obtained back in Question 11c.Suppose we didn’t have a preconceived notion that the right front tire would be
Write the null and alternative hypotheses for this new question.Suppose we didn’t have a preconceived notion that the right front tire would be chosen more oft en, but just wanted to find out if it
Conduct a simulation analysis to produce a simulated p-value. How does it compare to the p-value from the study of the class with 28 students? Is this what you expected? Explain.
Before you analyze the data, would you expect to find stronger evidence for the research conjecture (that people pick the right front tire more than one fourth of the time), weaker evidence, or the
If you were to repeat this study, what improvements might you make? What further research might you propose related to this topic in the future?
Now, let’s step back a bit and think about the scope of our inference. What are the wider implications? Do you think that your conclusion holds true for people in general? (These are extremely
Summarize the conclusion that you draw from this study and your simulation analysis. Also explain the reasoning process behind your conclusion.
What is the statistic that you can use to summarize the data collected in the study and what symbol is associated with this statistic?
Is there strong evidence against the null hypothesis for all three of the methods used in Question 11? Explain.
Let’s examine the strength of evidence with the three ways we used in Chapter 1.a. Determine the p-value from your simulation analysis. Also interpret what this p-value represents (i.e., the
Using the proportion of successes for the values on the horizontal axis, what is the center of your null distribution? Does it make sense that this is the center? Explain.
Use the One Proportion applet to simulate 1,000 repetitions of this study, assuming that every student in class selects randomly (equally) among the four tires. Report what values you input into the
Is it possible that we could observe 14 students from this class of 28 students even if all of the students were just selecting randomly among the four tires?To test this conjecture about the right
What percentage of the students picked the right front tire? Is this more than you would expect if students randomly pick one of the four tires?To test this conjecture about the right front tire, a
State the appropriate null and alternative hypotheses to be tested.To test this conjecture about the right front tire, a recent class of 28 students was asked, if they were in this situation, which
Describe the parameter of interest in words. (You can use the symbol Ï€ to represent this parameter.)To test this conjecture about the right front tire, a recent class of 28 students was
What is the variable that is measured/recorded on each observational unit?To test this conjecture about the right front tire, a recent class of 28 students was asked, if they were in this situation,
Reconsider the previous exercise. Notice that three different decimal numbers appear: 0.46, 0.484, and 0.50. Identify which is the null-hypothesized probability, which is the observed value of the
One of the authors once spun his tennis racquet 100 times and found that it landed with the label up for 46 of those 100 spins (0.46). For testing whether the probability (that a spun tennis racquet
Refer to the previous exercise. Th e researchers also found that 503 of the 1,770 people thought of the number 7. Do these data provide strong evidence that people have a tendency to select the
a. Describe the relevant parameter of interest.b. State the appropriate hypotheses to be tested.c. Calculate the observed value of the appropriate statistic.d. Check whether a theory-based approach
Lorena is a golfer who wants to investigate whether she successfully makes more than 60% of her 10-foot putts.a. Define (in words) the relevant parameter of interest for Lorena.b. State (in words and
Rick is a basketball player who wants to investigate whether he successfully makes more than 90% of his free throws by shooting with an underhand style.a. Define (in words) the relevant parameter of
Alfonso wants to investigate whether fewer than one-fourth of families with two children have two girls, so he collects data for 25 two-child families. Describe how he could use coins to perform a
Josephine wants to investigate whether more than one-third of families with two children have one child of each sex, so she collects data for 50 two-child families. Describe how she could use a die
Suppose that Sasha and Jayla both collect data to investigate whether people tend to call “heads” more often than “tails” when they are asked to call the result of a coin flip. If Sasha has a
Suppose that Jose and Roberto both collect data to investigate whether people tend to call “heads” more oft en than “tails” when they are asked to call the result of a coin flip. If Jose uses
Reconsider the previous exercise. Suppose that you were to define the parameter π, not as the probability that a New Zealand student would associate the name Tim with the face on the left , but as
a. Express the appropriate null and alternative hypotheses, in symbols and in words, for testing whether New Zealand students have a tendency to associate the name Tim with the face on the left.b.
Additional information supplied in the Sports Illustrated article was that 34.6% of all professional baseball players are from Latin-American countries, but 368 of the 595 (61.8%) players suspended
a. One question is whether 0.346, the observed proportion of PED-suspended players from the U.S., is (statistically) significantly less than 0.573, the proportion of all players from the U.S. Before
On the television show Mythbusters, the hosts Jamie and Adam wanted to investigate which side buttered toast prefers to land on when it falls through the air. To replicate a piece of toast falling
A statistics professor is in a fantasy golf league with four friends. Each week one of the five people in the league is the winner of that week’s tournament. During the 2010 season, this particular
The standard deviation of a null distribution is calculated using which value: the probability value in the null hypothesis or the observed value of the sample proportion?
A p-value is calculated assuming that which hypothesis is true: null or alternative?
Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins.
It also seemed to the author that ones showed up less often than what they should if the dice were fair and he wanted to test this. In his 500 dice rolls, 72 resulted in ones.a. Describe what the
It seemed to the author that sixes showed up more than what they should if the dice were fair and he wanted to test this. He had the machine roll 500 dice and obtained 92 sixes.a. Describe what the
The researchers found that of the 272 boxing matches, the competitor in red won 150 times.a. State the appropriate null and alternative hypotheses in the context of this study.b. Using an appropriate
The researchers found that of the 457 matches, the competitor in red won 248 times.a. State the appropriate null and alternative hypotheses in the context of this study.b. Using an appropriate
In Example 1.4, we explored whether voters make decisions based on a candidate’s facial appearance. The researchers described how they had people determine which of two candidates for the U.S.
Reconsider Exploration 1.3, where we explored whether the long-run proportion that students in a class would correctly assign the names Bob and Tim to the pictures. We tested to see if this long-run
Based on the statistics from the previous question where people were playing rock-paper-scissors, we want to see if players start with rock with a probability that is different than 1/3.a. State the
a. State the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols.b. Using an appropriate applet, find the p-value using a theory-based test
Recall Exercise 1.2.19, where researchers investigated whether rhesus monkeys have some ability to understand gestures made by humans. In one part of the study, they found that 31 of 40 monkeys
Recall Exercise 1.2.16, in which researchers asked 40 heterosexual couples which person said “I love you first.”They found that the man said “I love you” in 28 of the 40 couples before the
In the same research article, Utts (1995) also cites research from Morris et al. (1995) where, out of 97 Ganzfeld sessions, the receiver could correctly identify the image sent 2 times. You
a. Describe what the symbol π stands for in this context.b. State your null and alternative hypotheses.c. If the subjects in these studies have no psychic ability, approximately what proportion will
Recall that, to explore more deeply, the researchers went on to look at data from the most recent 361 heart transplantations at St. George€™s and found that 71 had resulted in deaths within
a. According to the dotplot produced by the applet, what is the mean of the null distribution? Explain how you could have anticipated this.b. According to the dotplot produced by the applet, is the
According to researchers, a coin fl ip may not have a 50% chance of landing heads and a 50% chance of landing tails. In fact, they believe that a coin is more likely to land the same way it started.
According to statistician Persi Diaconis, the probability of a penny landing heads when it is spun on its edge is only about 0.20. Suppose you doubt this claim and think that it should be more than
Suppose you ride to school with a friend and often arrive at a certain stop light when it is red. One day she states, €œIt seems like this light is green only 10% of the time when we get
What is a z-statistic?
Suppose you are using theory-based techniques (e.g., a one-proportion z-test) to determine p-values. How will a two-sided p-value compare to a one-sided p-value (assuming the one-sided p-value is
What is calculated using the formula (statistic − mean of null distr.)/(SD of null distr.)?
What is calculated using the formula √{π(1 − π)/n}?
Which sample size, n, gives the smallest standard deviation of the null distribution where the long-run proportion, π, is 0.25?A. 30 B. 40C. 50 D. 60
Would your answer change in Exercise 1.5.1 if the sample size were 100?In exercise 1.5.1Which long-run proportion of success, π, gives the largest standard deviation of the null distribution when
Which long-run proportion of success, π, gives the largest standard deviation of the null distribution when the sample size is 10?A. 0.05B. 0.25C. 0.50D. 0.90
Look at the figure long enough to follow each curve with your eye and recognize its shape and steepness. Keep these two facts in mind€”three shapes, two curves of each shape€”and
The six graphs are for two different sample sizes: one small (25) and one large (225). Your challenge in this exercise is to figure out how to tell the difference between a small-sample curve and a
Try to relate the shape of the curve to the alternate hypothesis.a. Suppose Buzz really wants to earn his fish and tries to guess right. Your alternative hypothesis is that Ï€ > 0.50. Th
Notice that the distance pˆ − π (x-axis) can tell you percent correct. Recall Example 1.1. For Buzz and Doris:a. A distance of 0.50 means Buzz is right _____% of the time.b. A distance of 0.00
Notice that there are three basic shapes for the curves: increasing, decreasing, and €œup-down.€ Tell the letters for each shape:a. Increasing:b. Decreasing:c. Up-down: 1.0 D 0.8
The graph below shows six different curves labeled A€“F. Each curve shows the relationship between the p-value (y-axis) and the distance pË† ˆ’ Ï€ (x-axis) for
In this exercise, as in the one before, we eliminate elections with more than two major party candidates as well as elections with two candidates of the same height. In addition, we eliminate the two
In the first election of the 20th century, The odore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28.Of these, 25 elections
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
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
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
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
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
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.
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
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
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,

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