As in Exercise 3, for each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values. 1. Seat-belt compliance in Massachusetts was 65% in 2008. The state wants to know if it has changed. 2. Last year, a survey found that 45% of the employees were willing to pay for on-site day care. The company wants to know if that has changed. 3. Regular card customers have a default rate of 6.7%. A credit card bank wants to know if that rate is different for their Gold card customers. 4. Regular card customers have been with the company for an average of 17.3 months. The credit card bank wants to know if their Gold card customers have been with the company on average the same amount of time.
> The Iliad also reports the cause of many injuries. Here is a table summarizing those reports for the 152 injuries for which the Iliad provides that information. Is there an association? 1. Under the null hypothesis, what are the expected values? 2. Compu
> Three statistics classes all took the same test. Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot.
> If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season (winter, spring, summer, and fall). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 w
> Consider the weights from Exercise 4. The side-by-side boxplots below show little difference between the two groups. Should this be sufficient to draw a conclusion about the accuracy of the weigh-in-motion scale?
> Thinking about the data on fuel efficiency in Exercise 3 , why is the blocking accomplished by a matched pairs analysis particularly important for a sample that has both cars and trucks?
> Find a 98% confidence interval of the weight differences in Exercise 4 . Interpret this interval in context.
> In Exercise 3, after deleting an outlying value of –27, the mean difference in fuel efficiencies for the 632 vehicles was 7.37 mpg with a standard deviation of 2.52 mpg. Find a 95% confidence interval for this difference and interpret it in context.
> The calibration test for a new weight-in-motion method of weighing trucks was introduced in Chapter 6, exercise 52 . Is this method consistent with the traditional method of static weighing? Are the conditions for matched pairs inference satisfied? Weigh
> We have data on the city and highway fuel efficiency of 633 cars and trucks. 1. Would it be appropriate to use paired t methods to compare the city fuel efficiency of the cars and the trucks? 2. Would it be appropriate to use paired t methods to compare
> Which of the following scenarios should be analyzed as paired data? 1. Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives. 2. 50 insomnia patients are given a placebo and 50 are
> Which of the following scenarios should be analyzed as paired data? 1. Students take an MCAT prep course. Their before and after scores are compared. 2. 20 male and 20 female students in class take a midterm. We compare their scores. 3. A group of colleg
> The researchers from Exercise 1 want to test if the proportions of foreign born are the same in the United States and Canada. What is the appropriate standard error to use for the hypothesis test? 1. What is the difference in the proportions of foreign b
> Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in order (January=1): 1. In what month was the highest ozone level eve
> If the information in Exercise 2 is to be used to make inferences about all people who work at non-profits and for-profit companies, what conditions must be met before proceeding? List them and explain if they are met.
> If the information in Exercise 1 is to be used to make inferences about the proportion all Canadians and all U.S. citizens born in other countries, what conditions must be met before proceeding? Are they met? Explain.
> For the interval given in Exercise 4 , explain what 95% confidence means.
> For the interval given in Exercise 3 , explain what 95% confidence means.
> The researchers from Exercise 2 created a 95% two-proportion confidence interval for the difference in those who are highly satisfied when comparing people who work at non-profits to people who work at for-profit companies. Interpret the interval with a
> The information in Exercise 1 was used to create a 95% two-proportion confidence interval for the difference between Canadians and U.S. citizens who were born in foreign countries. Interpret this interval with a sentence in context. 95% confidence  int
> Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 4
> The researchers in Exercise 12 decide to test the hypothesis. The degrees of freedom formula gives 51.83 df. Test the null hypothesis at α=0.05. Is the alternative one- or two-sided?
> The researchers in Exercise 11 decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 162.75 df. Test the null hypothesis at α=0.05.
> Using the summary statistics provided in Exercise 12 , the sports reporter calculated the following 95% confidence interval for the mean difference between major league baseball players and professional football players. The 95% interval for μMLB−μNF
> The full series of data giving the median age at first marriage in the United States for men and women shows the following pattern. 1. In what way do these data differ from standard time series? 2. Describe the patterns you see here. 3. Do you expect the
> Using the summary statistics provided in Exercise 11 , researchers calculated a 95% confidence interval for the mean difference between Walmart and Target purchase amounts. The interval was ($14.15, $1.85). Explain in context what this interval means.
> A sports reporter suggests that professional baseball players must be, on average, older than professional football players, since football is a contact sport and players are more susceptible to concussions and serious injuries. Using data from sports.ya
> Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores.
> Non-profits test Complete the analysis begun in Exercise 2 . 1. What is the difference in the proportions of the two types of companies? 2. What is the value of the z-statistic? 3. What do you conclude at α=0.05?
> Suppose an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country (www.unitednorthamerica.org/simdiff.htm). Similarly, 170 out of 1250 U.S. citizens reported being foreign-born. Find the standard error of the d
> Public health officials believe that 98% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 97.4% had been vaccinated. A statistician w
> For each of the following situations, find the critical value for z or t. 1. H0:μ=105 vs. HA:μ‰ 105 at α=0.05;n=61. 2. H0:p=0.05 vs. HA:p>0.05 at α=0.05. 3. H0:p=0.6 vs. HA:p‰ 0.6 at α=0.01. 4. H0:p=0.5 vs. HA:p
> For each of the following situations, find the critical value(s) for z or t. 1. H0:p=0.5 vs. HA:p‰ 0.5 at α=0.05. 2. H0:p=0.4 vs. HA:p>0.4 at α=0.05. 3. H0:μ=10 vs. HA:μ‰ 10 at α=0.05;n=36. 4. H0:p=0.5 vs. HA:p>0.5 at α=0.01;n=345. 5. H0:μ=20 vs.
> Which of the following statements are true? If false, explain briefly. 1. It is better to use an alpha level of 0.05 than an alpha level of 0.01. 2. If we use an alpha level of 0.01, then a P-value of 0.001 is statistically significant. 3. If we use an a
> Which of the following statements are true? If false, explain briefly. 1. Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis. 2. The alpha level depends on the sample size. 3. With an alpha level of 0.01, a P-value o
> Describe what these boxplots tell you about the relationship between the number of cylinders a car engine has and the car fuel economy (mpg).
> Which of these scatterplots show 1. little or no association? 2. a negative association? 3. a linear association? 4. a moderately strong association? 5. a very strong association?
> Which of the following are true? If false, explain briefly. 1. A very low P-value provides evidence against the null hypothesis. 2. A high P-value is strong evidence in favor of the null hypothesis. 3. A P-value above 0.10 shows that the null hypothesis
> Which of the following are true? If false, explain briefly. 1. A very high P-value is strong evidence that the null hypothesis is false. 2. A very low P-value proves that the null hypothesis is false. 3. A high P-value shows that the null hypothesis is t
> Which of the following are true? If false, explain briefly. 1. If the null hypothesis is true, you’ll get a high P-value. 2. If the null hypothesis is true, a P-value of 0.01 will occur about 1% of the time. 3. A P-value of 0.90 means that the null hypot
> For each of the following situations, state whether a Type I, a Type II, or neither error has been made. 1. A test of H0:μ=25 vs. HA:μ>25 rejects the null hypothesis. Later it is discovered that μ=24.9. 2. A test of H0:p=0.8 vs. HA:p
> For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly. 1. A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test H0:p=0.3 vs.
> A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 children in several differe
> Which of the following are true? If false, explain briefly. 1. A P-value of 0.01 means that the null hypothesis is false. 2. A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true. 3. A P-value of 0.01 is evidence against the nu
> Instead of advertising the percentage of customers who improve by at least 10 points, a manager suggests testing whether the mean score improves at all. For each customer they record the difference in score before and after taking the course (After Befor
> According to the 2010 Census, 11.4% of all housing units in the United States were vacant. A county supervisor wonders if her county is different from this. She randomly selects 850 housing units in her county and finds that 129 of the housing units are
> According to the 2010 Census, 16% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent surv
> In the first 17 years of the 21st century, did men and women marry at the same age? Here are boxplots of the age at first marriage for U.S. citizens then. Write a brief report discussing what these data show.
> A test preparation company claims that more than 50% of the students who take their GRE prep course improve their scores by at least 10 points. 1. Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain. 2. A test run wit
> Referring to the study of Exercise 1: 1. Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain. 2. The P-value from a clinical trial testing the hypothesis is 0.0028. What do you conclude? 3. What would you have conclud
> For each of the following situations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p =
> A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! State the null hypothesis for yo
> Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used cur
> Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evide
> The United States Golf Association (USGA) sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a
> A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.07. Explain in this context what the 7% represents.
> In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has incre
> Here are boxplots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2000 through 2018: 1. Compare the distribution of prices over the nineteen years. 2. Compare the stability of prices
> A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. What is th
> Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
> Using the t-tables, software, or a calculator, estimate 1. the critical value of t for a 95% confidence interval with df=7. 2. the critical value of t for a 99% confidence interval with df=102.
> Using the t-tables, software, or a calculator, estimate 1. the critical value of t for a 90% confidence interval with df=17. 2. the critical value of t for a 98% confidence interval with df=88.
> Suppose the store in Exercise 4 had 312 customers this Sunday. 1. Estimate the probability that the store revenues were at least $10,000. 2. If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst 10% of such
> The waiter in Exercise 3 usually waits on about 40 parties over a weekend of work. 1. Estimate the probability that he will earn at least $500 in tips. 2. How much does he earn on the best 10% of such weekends?
> A grocery store receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $20. 1. Explain why you cannot determine the probability that the next Sunday customer will spend at least $40. 2. Can
> A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of $9.60 and a standard deviation of $5.40. 1. Explain why you cannot determine the probability that a given party will tip him at least $20. 2.
> Based on meteorological data for the past century, a local TV weather forecaster estimates that the region average winter snowfall is 23", with a margin of error of ±2 inches. Assuming he used a 95% confidence interval, how should viewers interpret this
> After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562). Now the organization is trying to writ
> Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra: 1. Summarize the similarities and differences in their performance so far. 2. The coach can take only one player to the state championship. Whi
> A biology class conducts a bird count every week during the semester. Using the number of species counted each week, a student finds the following confidence interval for the mean number of species counted: Knowing that species have to be whole numbers,
> The LSAT (a test taken for law school admission) has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization
> Chapter 2, Exercise 16 showed the histogram of the European shoe sizes from a sample of 269 college students. Looking at the men only, a 95% confidence interval for the mean shoe size shows: The student knows that European shoes are sized only in whole a
> Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What wrong with the others? 1. t-interval for μ:with 90.00% Confidence,43454
> Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a ma
> A survey finds that a 95% confidence interval for the mean salary of a police patrol officer in Fresno, California, in 2016 is $52,516 to $53,509. A student is surprised that so few police officers make more than $53,500. Explain what is wrong with the s
> For the confidence interval you found in Exercise 11 , interpret this interval and explain what 95% confidence means in this context.
> In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value. 1. Suppose the standard deviation of the losses had been $3000 instead of $1500. What would the larger standard deviation do to the width of the con
> The housing market recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak i
> Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
> A National Vital Statistics Report (www.cdc.gov/nchs/) provides information on deaths by age, sex, and race. Below are displays of the distributions of ages at death for White and Black males: 1. Describe the overall shapes of these distributions. 2. How
> A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salm
> The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distributions of sample proportions from 1000 simulat
> For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. From past years, she guesses that about 10% of the class goes. Is it reasonable for her to use a Normal model for the s
> According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distri
> Gallup regularly conducts a poll using a Cantril scale, which asks respondents to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life, and rung 10 represents the best possible life. Respondents are asked what rung they would say the
> Pew Research, in 2015, polled a random sample of 1060 U.S. teens (ages 13–17) about Internet use. 56% of those teens reported going online several times a day a fact of great interest to advertisers. 1. Explain the meaning of p^=0.56 in the context of
> An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75
> When they send out their fundraising letters, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 2
> In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. 1. How many randomly selected employers must we contact in order to create an estimate in which we are 98%
> The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 400 people at random. 1. What proportion of the sample of 400 would you expect to be women? 2. What would the standard deviation of the sampling distri
> National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. Data from a sample of 39 male patients and 35 female patients on length of stay (in d
> It believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. 1. How many of this younger age group must we survey in order to estimate the proportion of no
> In Exercise 14, we saw that 53% of surveyed parents don’t spank their children. 1. Are the conditions for constructing a confidence interval met? 2. Would the margin of error be larger or smaller for 95% confidence? Explain.
> Consider the poll of Exercise 15. 1. Are the assumptions and conditions met? 2. Would the margin of error be larger or smaller for 95% confidence? Explain.
> The Gallup Poll described in Exercise 6 also asked about smoking. Only 18% of those polled reported that they smoked. 1. Calculate the margin of error for the proportion of all American adults who smoke with 99% confidence. 2. Explain in a simple sentenc
> An Ipsos/Reuters poll of 2214 U.S. adults voters in April and May 2017 asked a standard polling question of whether the United States was headed in the Right Direction or was on the Wrong Track. 54% said that things are on the wrong track vs. 33% who sai
> In a 2015 Pew Research study on trends in marriage and family (www.pewsocialtrends.org/2015/12/17/1-the-american-family-today/), 53% of randomly selected parents said that they never spank their children. The 95% confidence interval is from 50.6% to 55.4
> The 95% confidence interval for the number of teens in Exercise 5 who reported that they went online several times daily is from 53% to 59%. 1. Interpret the interval in this context. 2. Explain the meaning of 95% confident in this context.
> A machine is supposed to fill cans with 16 oz of soup. Of course, there will be some variation in the amount actually dispensed, and measurement errors are often approximately Normally distributed. The manager would like to understand the variability of
> The distribution of scores on a statistics test for a particular class is skewed to the left. The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximu
> The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples o
