Questions and Answers of Introductory Statistics Exploring The World Through Data

The acceptance rate for a random sample of 15 medical schools in the United States was taken. The mean acceptance rate for this sample was 5.77 with a standard error of 0.56. Assume the distribution
A random sample of 25 private universities was selected. A 95% confidence interval for the mean in-state tuition costs at private universities was (22,501, 32,664). Which of the following is a
A researcher collects one sample of 27 measurements from a population and wants to find a 95% confidence interval. What value should he use for t*? (Recall that df = n - 1 for a one-sample
A random sample of 30 12th-grade students was selected. The sample mean height was 170.7 centimeters, and the sample standard deviation was 11.5 centimeters.a. State how you would fill in the numbers
A random sample of 50 12th-grade students was asked how long it took to get to school. The sample mean was 16.2 minutes, and the sample standard deviation was 12. minutes.a. Find a 95% confidence
A random sample of 25 baseball players from the 2017 Major League Baseball season was taken and the sample data was used to construct two confidence intervals for the population mean. One interval
A body mass index (BMI) of more than 25 is considered unhealthy. The Minitab output given is from 50 randomly and independently selected people from the NHANES study.Test the hypothesis that the mean
In the United States, the population mean height for 10-year-old girls is 54.5 inches. Suppose a random sample of 15 10-year-old girls from Brazil is taken and that these girls had a sample mean
In the 2015 AFC Championship game, there was a charge the New England Patriots deflated their footballs for an advantage. The balls should be inflated to between 12.5 and 13.5 pounds per square inch.
In the 2015 AFC Championship game, there was a charge the New England Patriots deflated their footballs for an advantage. The Patriots’ opponents during the championship game were the Indianapolis
According to Deadline.com, the average price for a movie ticket in 2018 was $8.97. A random sample of movie prices in the San Francisco Bay Area 25 movie ticket prices had a sample mean of $12.27
According to Statista.com, the average price of a ticket to a Broadway show in 2017 was $109.21. A random sample of 25 Broadway ticket prices in 2018 had a sample mean of $114.7 with a standard
A 95% confidence interval for the ages of the first six presidents at their inaugurations is (56.2, 59.5). Either interpret the interval or explain why it should not be interpreted.
State whether each situation has independent or paired (dependent) samples.a. A researcher wants to compare food prices at two grocery stores. She purchases 20 items at Store A and finds the mean and
A random sample of 40 professional baseball salaries from 1985 through 2015 was selected. The league of the player (American or National) was also recorded. Salary (in hundred thousand dollars) and
Baseball Salaries In exercise 9.63 you could not reject the null hypothesis that the mean salary for the two leagues are the same, using a two-tailed test with a significance level of 0.05.a. If you
In exercise 9.64, you could reject the null hypothesis that the mean weights of soccer and baseball players were equal using a two-tailed test with a significance level of 0.05.a. If you found a 95%
The body temperatures of 65 men and 65 women were compared. The results of a hypothesis test are shown. Assume the conditions for using a t-test are satisfied.a. Why was a two-sample t-test used
Data were collected on calorie content in ales and IPAs and is summarized in the following table.a. Does the sample data provide evidence that there is a difference in calorie content for ales and
Heart rate data for a random sample of males and females was obtained. The data are available at the text’s website. Use the data to answer these questions. Data were originally published in the
A survey of asked respondents how long (in years) they thought it would be before self driving cars were the majority of vehicles on the road, and a random sample from this survey was selected. The
Assume women’s heights are approximately Normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. Which of the following questions can be answered using the Central
According to home-water-works.org, the average shower in the United States lasts 8.2 minutes. Assume the standard deviation of shower times is 2 minutes and the distribution of shower times is
Choose a test for each situation: one-sample t-test, two-sample t-test, paired t-test, and no t-test.a. A random sample of students who transfered to a 4-year university from community colleges are
Choose a t-test for each situation: one-sample t-test, two-sample t-test, paired t-test, and no t-test.a. A random sample of car dealerships is obtained. Then a student walks onto each dealer’s lot
A fast-food chain advertises that the mediumsize serving of French fries weighs 135 grams. A reporter took a random sample of 10 medium orders of French fries and weighed each order. The weights (in
A random sample of 12th-grade students were asked to rate the importance of reducing pollution on a scale from 0 to 1000. Responses were recorded by gender. The results of a hypothesis test are
Data were collected on calorie content for a random sample of ales and lagers and are summarized in the table. Assume the conditions for using a t-test are satisfied.a. If we wanted to use a
Data were collected on the weights of random samples of professional hockey players and professional baseball players.a. Using these descriptive statistics, can a two sample t-test be used to
The table shows the prices for identical groceries at two online grocery delivery services, Amazon and Walmart. Assume the sampling is random and the populations are Normal.a. Give the data, would a
The following table shows the heights (in inches) of a random sample of students and their parent of the same gender. Test the hypothesis that the mean for the students is more than the mean for the
The table shows the heights (in inches) of all the basketball players on the 2017–2018 Santa Clara University basketball team. Explain why it would be inappropriate to do a t test with these data.
a. In Chapter 8, you learned some tests of proportions. Are tests of proportions used for categorical or numerical data?b. In this chapter, you are learning to use chi-square tests. Do these tests
In Chapter 9, you learned some tests of means. Are tests of means used for numerical or categorical data?
A statistics student conducted a study in Ventura County, California, that looked at criminals on probation who were under 15 years of age to see whether there was an association between the type of
The table shows the raw data for the results of a student survey of 22 cars and whether they stopped completely at a stop sign or not. In the Color column, “Red” means the car was red, and
The table summarizes the outcomes of a study that students carried out to determine whether humanities students had a higher mean grade point average (GPA) than science students. Identify both of the
According to a 2017 report, 53% of college graduates in California had student loans. Suppose a random sample of 120 college graduates in California shows that 72 had college loans.a. What is the
According to a 2017 report, 64% of college graduate in Illinois had student loans. Suppose a random sample of 80 college graduates in Illinois is selected and 48 of them had student loans. a.
In a 2015 study by Nanney et al. and published in the Journal of American College Health, a random sample of community college students was asked whether they ate breakfast 3 or more times weekly.
According to the 2015 High School Youth Risk Behavior Survey, 41.5% of high school students reported they had texted or emailed while driving a car or other vehicle. Suppose you randomly sample 80
Fill in the blank by choosing one of the options given:Chi-square goodness-of-fit tests are applicable if the data consist of ___________ (one categorical variable, two categorical variables, one
Fill in the blank by choosing one of the options given:Chi-square goodness-of-fit data are often summarized with ____________ (one row or one column of observed counts—but not both, or at least two
In 2018 Pew Research reported that 11% of Americans do not use the Internet. Suppose in a random sample of 200 Americans, 26 reported not using the Internet. Using a chi-square test for
When playing Dreidel, (see photo) you sit in a circle with friends or relatives and take turns spinning a wobbly top (the dreidel). In the center of the circle is a pot of several foil-wrapped
The table shows the results of rolling a six-sided die 120 times.Test the hypothesis that the die is not fair. A fair die should produce equal numbers of each outcome. Use the four-step procedure
Repeat the chi-square test (all four steps) from exercise 10.23, but this time assume that you got exactly 20 outcomes in each of the six categories. Refer to the figure. Explain. NORMAL FLOAT AUTO
A 2018 Gallup poll asked college graduates if they agreed that the courses they took in college were relevant to their work and daily lives. The respondents were also classified by their field of
Treatment In a 2018 study by Zhu et al. reported in The Lancet, researchers conducted an experiment to determine the efficacy and safety of the drug dorzagliatin in the treatment of patients with
The table shows the percentage of all men and women in the United States aged 18 to 44 who meet aerobic fitness guidelines. Give two reasons why a chi-square test is not appropriate for this data.
The table shows the percentage of all U.S. households who are food secure, have low food security, or who have very low food security. The data are reported by area of residence. Give two reasons why
In a 2015 study reported in the Journal of American College Health, Cho et al. surveyed college students on their use of apps to monitor their exercise and fitness. The data are reported in the
A vaccine is available to prevent the contraction of human papillomavirus (HPV). The Centers for Disease Control and Prevention recommends this vaccination for all young girls in two doses. In a 2015
In the study described in 10.35 researchers also asked survey respondents if they had heard of the HPV vaccine. Data are shown in the table. Test the hypothesis that knowledge of the vaccine and race
The table shows the results of a two-way table of gender and whether a person is happy in his or her marriage, according to data obtained from a General Social Survey. Happiness of Marriage :
A 2018 Gallup poll asked respondents if they supported same-sex marriage. Results are reported by political party in the StatCrunch output that follows.a. Find the percentage in each political party
A 2018 Pew Research poll asked a random sample of Millennials and GenXers if they supported legalization of marijuana. Survey results found 70% of Millennials and 66% of GenXers supported marijuana
In a 2018 article published in The Lancet, Sprigg et al. studied the effect of tranexamic acid in treating patients with intracerebral hemorrhages using a randomized, placebo controlled trial. Of the
In a 2018 article published in The Lancet, Kappos et al. studied the effect of the drug siponimod in treating patients with secondary progressive multiple sclerosis (SPMS) using a double-blind,
A 2018 Pew Research poll recorded respondents political affiliation and education attainment. A summary of the data is shown in the following table. Test the hypothesis that political party
A 2018 Pew Research poll recorded respondents political affiliation and generation. A summary of the results for Millennials and GenXers are shown in the following table, assuming a sample size of
In a 2016 article published in the Journal of American College Health, Heller et al. surveyed a sample of students at an urban community college. Students’ ages and frequency of alcohol use per
The data in the table come from a General Social Survey. The top row is the number of children reported for the respondents. The respondents also reported their level of happiness; Very H means Very
In a 2009 study reported in the New England Journal of Medicine, Boyer et al. randomly assigned children aged 6 months to 18 years who had nonlethal scorpion stings to receive an experimental
In a 2015 study reported in the New England Journal of Medicine, Du Toit et al. randomly assigned infants who were likely to develop a peanut allergy (as measured by having eczema, egg allergies, or
In the study described in exercise 10.55, researchers (Du Toits et al., 2015) also studied infants with eczema, egg allergies, or both who also had a preexisting sensitivity to peanut extract. These
Suppose you have a random sample of firefighters in Illinois and want to determine if the racial distribution of the firefighters is different from the racial distribution of the state as a whole.
Suppose you know the class (first class, second class, third class, or steerage) and whether each person on the Titanic survived or died, for all passengers on the Titanic.
Suppose you take a random sample of students at a college, asking them their gender and in which of the following areas they are majoring: Fine Arts, Liberal Arts, Business, STEM (Science,
Suppose you randomly assign some parolees to check in once a week with their parole officers and others to check in once a month, and observe whether they are arrested within 6 months of starting
Based on a random sample of residents in a large city, you wish to determine if there is an association between income level (low, middle, or high) and whether the residents own or rent their home.
Suppose you are testing two different injections by randomly assigning them to children who react badly to bee stings and go to the emergency room. You observe whether the children are substantially
Suppose you are interested in whether more than 50% of voters in California support a proposition (Prop X). After the vote, you find the total number that support it and the total number that oppose
Suppose there is a theory that 90% of the people in the United States dream in color. You survey a random sample of 200 people; 198 report that they dream in color, and 2 report that they do not. You
In 2017 the Pew Research Center published a report on the demographics of the U.S. military. The following table shows the ethnic breakdown of active-duty U.S. military services and the ethnic
The following table shows the average number of vehicles sold in the United States monthly (in millions) for the years 2001 through 2018. Data on all monthly vehicle sales for these years were
An 2017 NPR/Marist poll asked a random sample of Americans if they had personally experienced sexual harassment in the workplace. The results are shown in the following table.a. Find the percentage
Three million people in Sweden are trained in CPR, which is more than 30% of the population. The data set is summarized below. A 2015 study by Hasselqvist-Ax et. al reported in the New England
Using your result from Exercise 7.107, solve for n by (1) dividing both sides of the equation by 2, (2) squaring both sides of the equation, (3) cross-multiplying, and (4) solving for n.
From Formula 7.2, an estimate for margin of error for a 95% confidence interval iswhere n is the required sample size and p̂ is the sample proportion. Since we do not know a value for p̂, we use a
A polling agency wants to determine the sample size required to get a margin of error of no more than 3 percentage points (0.03). Assume the pollsters are using a 95% confidence level. How large a
Has trust in the legislative branch of government declined? A Gallup poll asked U.S. adults if they trusted the legislative branch of government in 2008 and again in 2017. The results are shown in
Has trust in the executive branch of government declined? A Gallup poll asked U.S. adults if they trusted the executive branch of government in 2008 and again in 2017. The results are shown in the
Suppose a political consultant is hired to determine if a school bond is likely to pass in a local election. The consultant randomly samples 250 likely voters and finds that 52% of the sample
In the primaries leading up to the 2016 presidential election, the Business Insider reported that Bernie Sanders and Hilary Clinton were in a “statistical tie” in the polls leading up to the
In a 2018 survey conducted by Northeastern University, 28% of working adults with education levels less than a bachelor’s degree worried that their job would be eliminated due to new technology or
In 2018 Gallup reported that 52% of Americans are dissatisfied with the quality of the environment in the United States. This was based on a 95% confidence interval with a margin of error of 4
According to the Bureau of Labor Statistics, 71.9% of young women enroll in college directly after high school graduation. Suppose a random sample of 200 female high school graduates is selected and
According to a Gallup poll, 45% of Americans actively seek out organic foods when shopping. Suppose a random sample of 500 Americans is selected and the proportion who actively seek out organic foods
Pew Research reported that 46% of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that 37% of Americans got their news from local television.
In 2017, the journal Obesity reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed
A double-blind study using random assignment was done of pregnant women in Denmark. Women were given fish oil or a placebo during pregnancy. Their children were followed during the first 5 years of
Refer to Exercise 7.77 for information. This data set records results just for the boys.a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that
In 2016 and 2017 Gallup asked American adults about their amount of trust they had in the judicial branch of government. In 2016, 61% expressed a fair amount or great deal of trust in the judiciary.
In 2003 and 2017 Gallup asked Democratic voters about their views on the FBI. In 2003, 44% thought the FBI did a good or excellent job. In 2017, 69% of Democratic voters felt this way. Assume these
A Harris poll asked a sample of U.S. adults if they agreed with the statement “Artificial intelligence will widen the gap between the rich and poor in the U.S.” Of those aged 18 to 35, 69% agreed
A Harris poll asked Americans in 2016 and 2017 if they were happy. In 2016, 31% reported being happy and in 2017, 33% reported being happy. Assume the sample size for each poll was 1000. A 95%
In the 2018 study Closing the STEM Gap, researchers wanted to estimate the percentage of middle school girls who planned to major in a STEM field.a. If a 95% confidence level is used, how many people
Pew Research conducted a study in 2018 to estimate the percentage of Americans who do not use the Internet.a. If a 95% confidence level is used, how many people should be included in the survey if
Of 1019 U.S. adults responding to a 2017 Harris poll, 47% said they always or often read nutrition labels when grocery shopping.a. Construct a 95% confidence interval for the population proportion of

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