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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypotheses,
Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypotheses,
Construct a 95% confidence interval for a population proportion using repeated tests of significance to develop an interval of plausible values based on a sample proportion of 0.52 from a sample of
In a May 2013 Gallup poll based on a representative sample of 1,535 adult Americans, 53% responded that they thought same-sex marriages should be legal and have the same rights as traditional
The previous question gave the results of the Gallup poll where 53% of a sample of 1,535 adult Americans responded that they thought same-sex marriages should be legal and have the same rights as
Construct a 95% confidence interval for a population proportion using repeated tests of significance to develop an interval of plausible values based on a sample proportion of 0.52 from a sample of
Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a population you feel you can generalize your conclusions to?
Was the sampling method unbiased?
Was the sample random?
Do you feel comfortable generalizing your conclusions to all cell phone users? If not, is there a population (broader than the sample) you feel you can generalize your conclusions to?
Was the sampling method unbiased?
Was the sample random?
Refer to Exercise 2.CE.9.a. Based on the test results found in Exercise 2.CE.9, part (b), if you are testing at a significance level of 5% and you have made an error, what type of error have you
Body temperatures were measured on a random sample of 20 females and 20 males applying for health insurance. Together, their average temperature was 98.8°F with a standard deviation of 0.2°F.a. Are
Biased samples either overestimate or underestimate the parameter of interest. List the samples from Exercise 2.CE.7 you think might overestimate the following parameters.a. Average student GPAb.
Which samples do you think are nonbiased samples of the population of all students at a college/fouryear university? If it is a biased sample, is there a different population for which you believe
Refer to Exercise 2.CE.5. Suppose you are testing to see if the population proportion of all brides who keep their own name is different from 15%.a. If testing at a significance level of 5%, would
What percentage of U.S. brides keep their own names after marriage, as opposed to taking their husband’s name or using some modification (such as hyphenation) of her name and her husband’s?
A study published in 2009 (Goldstein et al., 2009) involved a sample of 499 adults selected from various regions across the country of Israel. These adults were approached by interviewers in public
A reader wrote in to the “Ask Marilyn” column in Parade magazine to say that his grandfather told him that in three-fourths of all baseball games, the winning team scores more runs in one inning
Suppose that you select a sample of students at your university by standing in front of the library and asking students who pass by to take a survey.a. Would this be a simple random sample from the
Suppose that you select Major League Baseball (MLB) games played during the second week in April as a sample of all MLB games played in the upcoming season.a. Would this be a simple random sample?
Explain, as if to someone who doesn’t know much about statistics, why it’s dangerous to reach dramatically different conclusions for p-values of 0.04999 and 0.50001 obtained on the same dataset.
Reconsider Example 1.5 about whether trick-or treaters have an overall preference between Halloween toys or candy.a. Describe what Type I error means in this context.b. Describe what Type II error
Reconsider Example 1.4 about whether winners of elections can be predicted better than random chance simply by considering the faces of the candidates.a. Describe what Type I error means in this
Example P.1 describes a study that compared proportions of people who agreed to become organ donors, depending on the type of default option used. The null hypothesis is that all three default
Later in the book you will encounter hypotheses of the following type:H0: Men and women do not differ on average with regard to the variable of interest.Ha: Men and women do diff er on average with
Later in the book you will encounter many hypotheses of the following type:H0: New treatment is no better than current treatment.Ha: New treatment is better than current treatment.a. Describe what
Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses
Lie detector tests are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be
As with a jury trial, another analogy to hypothesis testing involves medical diagnostic tests. These tests aim to indicate whether or not the patient has a particular disease. But the tests are not
Suppose that you are considering whether to publish a weekly alternative newspaper on campus. You decide to survey a random sample of students on your campus to ask if they would be likely to read
Recall that the two errors discussed in this chapter were regarded as “false alarm” and “missed opportunity.” In some fields, these errors are also regarded as “consumer’s risk” and
Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor
The significance level α determines the probability of making a Type I error. Errors are bad. So, why don’t we always set ???? to be extremely small, such as 0.0001?
Reconsider Harley the dog from Exploration 1.1 and the previous exercise. We found that the observed data provided very strong evidence that Harley the dog was doing better than random chance. Which
In Exploration 1.1, we looked at a study to investigate whether Harley the dog could select the correct cup more than 50% of the time in the long run.a. Describe what a Type I error would be in this
Reconsider dolphins Buzz and Doris from Example 1.1 and the previous exercise. We found that the observed data provided very strong evidence that Doris and Buzz were actually communicating better
In Example 1.1, we looked at a study to investigate whether dolphins could communicate. In doing so, we tested whether Buzz, one of the dolphins, could push the correct button more than 50% of the
A researcher decides to set the significance level to 0.10.a. If the null hypothesis is true, what is the probability of a Type I error?b. If the researcher chooses a smaller significance level, what
A researcher decides to set the significance level to 0.001.a. If the null hypothesis is true, what is the probability of a Type I error?b. If the researcher chooses a larger significance level, what
Suppose that you perform a significance test and obtain a p-value of 0.036.a. For what significance levels α would you reject the null hypothesis?b. For what significance levels α would you fail to
Suppose that you perform a significance test using the α = 0.05 significance level.a. For what p-values would you reject the null hypothesis?b. For what p-values would you fail to reject the null
Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the α = 0.01 significance level. Th en suppose that your colleague decides to conduct
Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the α = 0.05 significance level. Then suppose that your colleague decides to conduct
Indicate whether or not you would reject the null hypothesis, with a p-value of 0.064, for the following significance levels.a. α = 0.05 b. α = 0.10c. α = 0.01 d. α = 0.065
Indicate whether or not you would reject the null hypothesis, at the α = 0.05 significance level, for the following p-values.a. p-value = 0.078 b. p-value = 0.045c. p-value = 0.001 d.
Suppose that we conduct a test of significance using 5% as our level of significance.a. What is the probability of making a Type I error (if the null hypothesis is true)?b. Suppose we conduct 10
In your own words, explain the concept of degrees of freedom as it relates to t-distributions, including discussion of how a t-distribution begins to look like a normal distribution as the degrees of
In your own words, explain why (mean − median)/SD is a good measure of skewness.
Normal (or average) body temperature of humans is often thought to be 98.6°F. Is that number really the average body temperature for human males? To test this, we will use the MaleTemps data set
The data set MaleTemps (found on the textbook website) consists of 65 body temperatures from healthy male volunteers aged 18 to 40 that were participating in vaccine trials. Put this data set into
Consider the investigation of the manufacturing process that is producing hypodermic needles. Recall that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a
According to a Pew Research Center report from 2012, the average commute time to work in California is 27.5 minutes. To investigate whether a different average is true for the small city that she
In the same study as was mentioned in the previous two exercises, data were also collected on 65 healthy female volunteers aged 18 to 40 that were participating in the vaccine trials. Th e data set
Consider the investigation of the manufacturing process that is producing hypodermic needles.a. Describe how you can conduct a simulation-based test of significance to investigate whether the data
Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor
Reconsider the study about one of the authors wanting to find out whether the SPF of sunscreens used by students at her school (which is in a very sunny part of the U.S.) exceeds 30, on average.a. In
Reconsider the study about one of the authors wanting to find out whether the SPF of sunscreens used by students at her school (which is in a very sunny part of the U.S.) exceeds 30, on average.a.
According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State
Most dermatologists recommend using sunscreens that have a sun protection factor (SPF) of at least 30. One of the authors wanted to find out whether the SPF of sunscreens used by students at her
Reconsider Dr. Sameer’s research question about how much time Cal Poly students spend on watching television, and recall that for the random sample of 100 Cal Poly students’ number of hours per
a. Suppose that on analyzing the data from the survey of a random sample of 100 Cal Poly students, the p-value for Dr. Sameer’s study was computed to be 0.16. Interpret what this p-value means in
Reconsider Dr. Sameer€™s research question about how much time Cal Poly students spend on watching television. Suppose that Dr. Sameer surveys a random sample of 100 Cal Poly students, and
Reconsider Dr. Sameer’s research question about how much time Cal Poly students spend on watching television. Suppose that for the random sample of 100 Cal Poly students the mean number of hours
Students in a statistics class were asked the cost of their last haircut. Th e data set can be found on the textbook website as HaircutCosts. Put this data set into the Descriptive Statistics applet
In which scenario would you expect to see more variability in the data: heights of a random sample of 100 college students or heights of a random sample of 500 college students?A. Random sample of
Suppose that birth weights of babies in the U.S. have a mean of 3250 grams and standard deviation of 550 grams. Based on this information, which of the following is more unlikely? Circle one.A. A
An instructor collected data on the number of states students in her class have visited in the U.S. A dotplot for the collected data is shown below.a. Identify the observational units.b. Identify the
a. Suppose that an instructor decides to add five points to every student’s exam score in a class. What effect would this have on the mean exam score for the class? On the median exam score?
Reconsider the previous exercise where the monthly salaries of the three people working in a small firm are $3500, $4000, and $4500. If instead of a $100 raise, everyone gets a 10% raise, how, if at
Reconsider the previous exercise. The monthly salaries of the three people working in a small firm are $3,500, $4,000, and $4,500. Suppose the firm makes a profit and everyone gets a $100 raise. How,
On January 28, 1986, the Space Shuttle Challenger broke apart 73 seconds into its flight, killing all seven astronauts on board. All investigations into reasons for the disaster pointed towards the
The monthly salaries of the three people working in a small firm are $3,500, $4,000, and $4,500. Suppose the firm makes a profit and everyone gets a $100 raise. How, if at all, would the average of
Referring to Example 1.1 about Doris and Buzz, explain where randomization occurs in your chance model but may not be truly random chance in the study.
Referring to Example 1.1. about Doris and Buzz, explain where randomization could come into play in the study design.
True or false? Increasing the sample size n, always helps improve the bias in the sample. Explain.
Explain, as if to someone who doesn’t know statistics, why taking a random sample of only 1500 people from a very large population is representative, even of rare subpopulations.
In the previous exercise, explain whether or not you believe the sample is representative of the population of interest and why.In order to understand reasons why consumers visit their store, a local
Identify each of the following by describing it or stating its value (where possible).a. Population of interestb. Samplec. Parameter of interestd. StatisticIn order to understand reasons why
In the previous exercise, explain whether or not you believe the sample is representative of the population of interest and why.In order to investigate how many hours a day students at their school
Identify each of the following by describing it or stating its value (where possible).a. Population of interestb. Samplec. Parameter of interestd. StatisticIn order to investigate how many hours a
Consider how the sample for the study was selected. If the study was conducted by taking a random sample, explain (in enough detail that someone could follow your directions to obtain the sample) how
Among the sample, the information for three particular sharks is given here:(i) Shark 1 had the disease and had a blood oxygen level of 1.2%.(ii) Shark 2 did not have the disease and had a blood
Because the disease affects a shark’s ability to extract oxygen from the water, the zoologist also measures the shark’s blood oxygen content. Th e zoologist finds that, on average, shark’s
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 zoologist wishes to test whether there is evidence that less than one-fourth of the sharks in the aquarium are diseased.a. State the null and alternative hypotheses for this test.b. What is the
Use the previous information to answer the following questions about the study.a. Identify the variable measured on each shark.b. Is the variable categorical or quantitative?c. Identify at least one
Use the previous information to answer the following questions about the shark 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.a. What is the population of interest?b. Do you believe that the proportion of diseased sharks in the sample is likely less than,
Consider how the sample for the study was s elected. If the study was conducted by taking a random sample, explain (in enough detail that someone could follow your directions to obtain the sample)
Among the sample, the information for three particular respondents is given here:(i) Respondent 1 reported spending 240 minutes in the last three days reading/watching news coverage about the trial
The survey also asked participants to report the time the respondent spent reading or watching news coverage about the trial during the last three days. The poll found that, on average, respondents
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 news program wishes to test whether there is evidence that more than three-quarters of U.S. adults are opposed to the verdict. Five hundred and sixty two participants participated in the survey,
Use the previous information to answer the following questions about the news program.a. Identify the variable measured on each participant in the survey.b. Is the variable categorical or
Use the previous information to answer the following questions about the news program survey.a. Describe in words the parameter of interest.b. Identify the numeric value of the statistic
Use the previous information to answer the following questions.a. What is the population of interest?b. Do you believe that the proportion of people unhappy with the verdict in the sample is
Consider how the sample was selected for the study. If the study was conducted by taking a random sample, explain (in enough detail that someone could follow your directions to obtain the sample) how
Among the sample, the information for three particular likely voters is given here:(i) Likely voter 1 reported spending 0 minutes in the last week learning/reading about local politics and likely

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