Question: When comparing two sample proportions with a

> Suppose college men’s heights are approximately Normally distributed with a mean of 70.0 inches and a population standard deviation of 3 inches. What height is at the 20th percentile? Include an appropriately labeled Normal curve to support your answer.

> Suppose college women’s heights are approximately Normally distributed with a mean of 65 inches and a population standard deviation of 2.5 inches. What height is at the 20th percentile? Include an appropriately labeled sketch of the Normal curve to suppo

> The distribution of grade point averages GPAs for medical school applicants in 2017 were approximately Normal, with a mean of 3.56 and a standard deviation of 0.34. Suppose a medical school will only consider candidates with GPAs in the top 15% of the ap

> A 20-question multiple choice quiz has five choices for each question. Suppose that a student just guesses, hoping to get a high score. The teacher carries out a hypothesis test to determine whether the student was just guessing. The null hypothesis is p

> Scores on the 2017 MCAT, an exam required for all medical school applicants, were approximately Normal with a mean score of 505 and a standard deviation of 9.4. a. Suppose an applicant had an MCAT score of 520. What percentile corresponds with this score

> The weight of newborn hippopotami is approximately Normal, with a mean of 88 pounds and a standard deviation of 10 pounds. a. What is the probability that a newborn hippo weighs between 90 and 110 pounds? b. Suppose baby hippos that weigh at the 5th perc

> A manager at a casual dining restaurant noted that 15% of customers ordered soda with their meal. In an effort to increase soda sales, the restaurant begins offering free refills with every soda order for a two-week trial period. During this trial period

> The National Association for Law Placement estimated that 86.7% of law school graduates in 2015 found employment. An economist thinks the current employment rate for law school graduates is different from the 2015 rate. Pick the correct pair of hypothese

> In 2016, the Centers for Disease Control and Prevention estimated that the flu vaccine was 73% effective against the influenza B virus. An immunologist suspects that the current flu vaccine is less effective against this virus. Pick the correct pair of h

> A friend is tested to see whether he can tell bottled water from tap water. There are 30 trials (half with bottled water and half with tap water), and he gets 18 right. a. Pick the correct null hypothesis: i. pn = 0.50 ii. pn = 0.60 iii. p = 0.50 iv. p =

> According to a 2015 University of Michigan poll, 71.5% of high school seniors in the United States had a driver’s license. A sociologist thinks this rate has declined. The sociologist surveys 500 randomly selected high school seniors and finds that 350 h

> A college chemistry instructor thinks the use of embedded tutors (tutors who work with students during regular class meeting times) will improve the success rate in introductory chemistry courses. The passing rate for introductory chemistry is 62%. The i

> In 2016 a Harris poll estimated that 3.3% of American adults are vegetarian. A nutritionist thinks this rate has increased and will take a random sample of American adults and record whether or not they are vegetarian. State the null and alternative hypo

> In problem 8.16, a college chemistry instructor thinks the use of embedded tutors will improve the success rate in introductory chemistry courses. The instructor carried out a hypothesis test and found that the observed value of the test statistic was 2.

> A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is 17%. A hospital was interested in knowing whether thei

> Choose one of the answers in each case. In statistical inference, measurements are made on a _____ (sample or population), and generalizations are made to a _____ (sample or population).

> In problem 8.15 the nutritionist was interested in knowing if the rate of vegetarianism in American adults has increased. She carried out a hypothesis test and found that the observed value of the test statistic was 2.77. We can calculate that the p-valu

> A college chemistry instructor thinks the use of embedded tutors will improve the success rate in introductory chemistry courses. The passing rate for introductory chemistry is 62%. During one semester, 200 students were enrolled in introductory chemistr

> In 2016 the Harris poll estimated that 3.3% of American adults are vegetarian. A nutritionist thinks this rate has increased. The nutritionist samples 150 American adults and finds that 11 are vegetarian. a. What is pn, the sample proportion of vegetaria

> According to Green Car Reports, 4.4% of cars sold in California in 2017 were hybrid cars. Suppose in a random sample of 500 recently sold cars in California 18 were hybrid. a. Write the null and alternative hypotheses to test that hybrid car sales in Cal

> According to a 2017 Pew Research Center report, 37% of adults aged 18 to 29 had student loan debt. Suppose in a random sample of adults from this age group 48 out of 120 had student loan debt. a. Give the null and alternative hypotheses to test that the

> An economist is testing the hypothesis that the employment rate for law school graduates is different from 86.7%. The economist is using a 5% significance level and these hypotheses: H0: p = 0.867 and Ha: p  0.867. Explain what the 5% significance level

> An immunologist is testing the hypothesis that the current flu vaccine is less than 73% effective against the flu virus. The immunologist is using a 1% significance level and these hypotheses: Ho: p = 0.73 and Ha: p 6 0.73. Explain what the 1% significan

> The label on a can of mixed nuts says that the mixture contains 40% peanuts. After opening a can of nuts and finding 22 peanuts in a can of 50 nuts, a consumer thinks the proportion of peanuts in the mixture differs from 40%. The consumer writes these hy

> Choose one of the answers given. The null hypothesis is always a statement about a _____ (sample statistic or population parameter).

> Quantitative SAT scores are approximately Normally distributed with a mean of 500 and a standard deviation of 100. On the horizontal axis of the graph, indicate the SAT scores that correspond with the provided z-scores. (See the labeling in Exercise 6.14

> In 2017 Pew Research Center polled 3930 adults in the United States and found that 43% reported playing video games often on some kind of electronic device. a. Identify the population and the sample. b. What is the parameter of interest? What is the stat

> The city of San Francisco provides an open data set of commercial building energy use. Each row of the data set represents a commercial building. A sample of 100 buildings from the data set had a mean floor area of 32,470 square feet. Of the sample, 28%

> The standard deviation of all professional NBA basketball players is 29.9 pounds. A sample of 50 professional basketball players has a standard deviation of 26.7 pounds. Which number is σ, and which number is s?

> The mean weight of all professional NBA basketball players is 218.8 pounds. A sample of 50 professional basketball players has a mean weight of 217.6 pounds. Which number is µ, and which number is x ?

> Two symbols are used for the standard deviation: σ and s. a. Which represents a parameter, and which represents a statistic? b. To estimate the commute time for all students at a college, 100 students are asked to report their commute times in minutes. T

> Two symbols are used for the mean: µ and x. a. Which represents a parameter, and which a statistic? b. In determining the mean age of all students at your school, you survey 30 students and find the mean of their ages. Is this mean x or µ?

> Use the data given in Exercise 7.23. Make the two given tables into one table by combining men for capital punishment into one group, men opposing it into another, women for it into one group, and women opposing it into another. Show your two-way table.

> The website scholarshipstats.com collected data on all 5341 NCAA basketball players for the 2017 season and found a mean height of 77 inches. Is the number 77 a parameter or a statistic? Also identify the population and explain your choice.

> To determine if patrons are satisfied with performance quality, a theater surveys patrons at an evening performance by placing a paper survey inside their programs. All patrons receive a program as they enter the theater. Completed surveys are placed in

> A school district conducts a survey to determine whether voters favor passing a bond to fund school renovation projects. All registered voters are called. Of those called, 15% answer the survey call. Of those who respond, 62% say they favor passing the b

> Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a coin, and if the coin comes up heads, then he or she is in your sample. Explain why this is not a good method.

> Assume your class has 30 students and you want a random sample of 10 of them. Describe how to randomly select 10 people from your class using the random number table.

> The Centers for Disease Control and Prevention (CDC) conducts an annual Youth Risk Behavior Survey, surveying over 15,000 high school students. The 2015 survey reported that, while cigarette use among high school youth had declined to its lowest levels,

> You need to select a simple random sample of two from six friends who will participate in a survey. Assume the friends are numbered 1, 2, 3, 4, 5, and 6. Use technology to select your random sample. Indicate what numbers you obtained and how you interpre

> You need to select a simple random sample of four from eight friends who will participate in a survey. Assume the friends are numbered 1, 2, 3, 4, 5, 6, 7, and 8. Select four friends, using the two lines of numbers in the next column from a random number

> Is simple random sampling usually done with or without replacement?

> The city of Chicago provides an open data set of the number of WiFi sessions at all of its public libraries. For 2014, there were an average of 451,846.9 WiFi sessions per month at all Chicago public libraries. What is the correct notation for the value

> Eric wants to go skiing tomorrow, but only if there are 3 inches or more of new snow. According to the weather report, any amount of new snow between 1 inch and 6 inches is equally likely. The probability density curve for tomorrow’s ne

> Ondansetron (Zofran) is a drug used by some pregnant women for nausea. There was some concern that it might cause trouble with pregnancies. An observational study was done of women in Denmark (Pasternak et al. 2013). An analysis of 1849 exposed women and

> 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 should be included in the survey if the researchers w

> 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 the researchers wanted to have a margin of error of 6%?

> The website www.mlb.com compiles statistics on all professional baseball players. For the 2017 season, statistics were recorded for all 663 players. Of this population, the mean batting average was 0.236 with a standard deviation of 0.064. Would it be ap

> St. Louis County is 24% African American. Suppose you are looking at jury pools, each with 200 members, in St. Louis County. The null hypothesis is that the probability of an African American being selected into the jury pool is 24%. a. How many African

> When comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, will you get a smaller p-value if the sample proportions are close together or if they are far apart? Explain.

> A random sample of likely voters showed that 49% planned to support Measure X. The margin of error is 3 percentage points with a 95% confidence level. a. Using a carefully worded sentence, report the 95% confidence interval for the percentage of voters w

> A 2017 Gallup poll found that 601 out of 1018 randomly selected adults in the United States said protection of the environment should be given priority over development of U.S. energy supplies such as coal, oil, and gas. Assuming the conditions for using

> A recent Monmouth University poll found that 675 out of 1008 randomly selected people in the United States felt that college and universities with big sports programs placed too much emphasis on athletics over academics. Assuming the conditions for using

> Professional basketball LeBron James is a 74% free-throw shooter. Assume that free throw shots are independent. Suppose, over the course of a season, James attempts 600 free throws. a. Find the mean and the standard deviation for the expected number of f

> According to the Pew Research Center, 53% of millennials (those born between 1981 and 1997) reported using a library or bookmobile within the last year. Suppose that a random sample of 200 millennials is taken. a. Complete this sentence: We would expect

> A weight-loss diet claims that it causes weight loss by eliminating carbohydrates (breads and starches) from the diet. To test this claim, researchers randomly assign overweight subjects to two groups. Both groups eat the same amount of calories, but one

> A magazine advertisement claims that wearing a magnetized bracelet will reduce arthritis pain in those who suffer from arthritis. A medical researcher tests this claim with 233 arthritis sufferers randomly assigned either to wear a magnetized bracelet or

> A 2017 Pew Research Center report on drones found that only 24% of Americans felt that drones should be allowed at events, like concerts or rallies. Suppose 100 Americans are randomly selected. a. What is the probability that exactly 25 believe drones sh

> Suppose you are testing someone to see whether she or he can tell Coke from Pepsi, and you are using 20 trials, half with Coke and half with Pepsi. The null hypothesis is that the person is guessing. a. About how many should you expect the person to get

> The use of drones, aircraft without onboard human pilots, is becoming more prevalent in the United States. According to a 2017 Pew Research Center report, 59% of American had seen a drone in action. Suppose 50 Americans are randomly selected. a. What is

> According to the Centers of Disease Control and Prevention, 44% of U.S. households still had landline phone service. Suppose a random sample of 60 U.S. households is taken. a. Find the probability that exactly 25 of the households sampled still have a la

> According to the Centers of Disease Control and Prevention, 52% of U.S. households had no landline and only had cell phone service. Suppose a random sample of 40 U.S. households is taken. a. Find the probability that exactly 20 the households sampled onl

> Colorado has a high school graduation rate of 75%. a. In a random sample of 15 Colorado high school students, what is the probability that exactly 9 will graduate? b. In a random sample of 15 Colorado high school students, what is the probability that 8

> Wisconsin has the highest high school graduation rate of all states at 90%. a. In a random sample of 10 Wisconsin high school students, what is the probability that 9 will graduate? b. In a random sample of 10 Wisconsin high school students, what is the

> According to a survey conducted by OnePoll, a marketing research company, 10% of Americans have never traveled outside their home state. Assume this percentage is accurate. Suppose a random sample of 80 Americans is taken. a. Find the probability that mo

> According to data from the U.S. State Department, the percentage of Americans who have a passport has risen dramatically. In 2007, only 27% of Americans had a passport; in 2017 that percentage had risen to 42%. Assume that currently 42% of Americans have

> According to the American Veterinary Medical Association, 30% of Americans own a cat. a. Find the probability that exactly 2 out of 8 randomly selected Americans own a cat. b. In a random sample of 8 Americans, find the probability that more than 3 own a

> According to the American Veterinary Medical Association, 36% of Americans own a dog. a. Find the probability that exactly 4 out of 10 randomly selected Americans own a dog. b. In a random sample of 10 Americans, find the probability that 4 or fewer own

> For each situation, identify the sample size n, the probability of a success p, and the number of success x. When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability. Assume

> Assume that college women’s heights are approximately Normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. On the horizontal axis of the graph, indicate the heights that correspond to the z-scores provid

> For each situation, identify the sample size n, the probability of a success p, and the number of success x. When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability. Assume

> Alaska Airlines has an on-time arrival rate of 88%. Assume that in one day, this airline has 1200 flights. Suppose we pick one day in December and find the number of ontime Alaska Airline arrivals. Why would it be inappropriate to use the binomial model

> Professional basketball player Draymond Green has a free-throw success rate of 70%. Suppose Green takes as many free throws as he can in one minute. Why would it be inappropriate to use the binomial model to find the probability that he makes at least 5

> In Exercise 6.59 you are told to assume that none of the children will be twins or other multiple births. Why? Which of the conditions required for a binomial experiment would be violated if there were twins?

> A die is rolled 5 times, and the number of spots for each roll is recorded. Explain why this is not a binomial experiment. Name a condition for use of the binomial model that is not met.

> A coin will be flipped four times, and the number of heads recorded. Explain why this is a binomial experiment. Check all four required conditions.

> A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is 0.50. Explain why

> When, in a criminal court, a defendant is found “not guilty,” is the court saying with certainty that he or she is innocent? Explain.

> When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?

> If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? Why or why not?

> Explain the difference between sampling with replacement and sampling without replacement. Suppose you have the names of 10 students, each written on a 3-inch by 5-inch notecard, and want to select two names. Describe both procedures.

> Is it acceptable practice to look at your research results, note the direction of the difference, and then make the alternative hypothesis one-sided in order to achieve a significant difference? Explain.

> A psychologist is interested in testing whether offering students a financial incentive improves their video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video

> Human blood is divided into 8 possible blood types. The rarest blood type is AB negative. Only 1% of the population has this blood type. Suppose a random sample of 50 people is selected. Can we find the probability that more than 3% of the sample has AB

> While the majority of people who are color blind are male, the National Eye Institute reports that 0.5% of women of with Northern European ancestry have the common form of red-green color blindness. Suppose a random sample of 100 women with Northern Euro

> Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. You use many bite-sized pieces selected randomly, half from buttered toast and half from toast with margarine. The taster is blindfolded.

> By establishing a small value for the significance level, are we guarding against the first type of error (rejecting the null hypothesis when it is true) or guarding against the second type of error?

> 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 percentages are based on samples of 1200 Democratic vote

> 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 with the statement. Of those aged 36 to 50, 60% agreed wit

> 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% confidence interval for the difference in these proportions p

> The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and one group did n

> Suppose you want to estimate the mean grade point average (GPA) of all students at your school. You set up a table in the library asking for volunteers to tell you their GPAs. Do you think you would get a representative sample? Why or why not?

> 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. Assume the sample size for each poll was 1200. a. Cons

> Statistics student Hector Porath wanted to find out whether gender and the use of turn signals when driving were independent. He made notes when driving in his truck for several weeks. He noted the gender of each person that he observed and whether he or

> 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 in a 24-hour period. The study was done in 2003 and rep

> 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 life to see if they developed asthma. The results are su

> 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 preschool was linked with a higher graduation rate? b. Verif

> The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and the other group

> 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 2017, 68% of Americans felt this way. These percenta

> According to a 2017 Gallup poll, 572 out of 1021 randomly selected smokers polled believed they are discriminated against in public life or in employment because of their smoking. a. What percentage of the smokers polled believed they are discriminated a