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 sampling distribution of the sample proportion? Why or why not?
> 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
> 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.
> 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
> 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
> Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont: 1. Which statistics would you use to identify the center and spread of this distribution? Why? 2. How many parks would you classify as outliers?
> An investment company is planning to upgrade the mobile access to their website, but they’d like to know the proportion of their customers who access it from their smartphones. They draw a random sample of 200 from customers who recently logged in and ch
> A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 452 exchange, so there are 10,000 possible numbers from 452-0000
> A large hospital has an average of 7 fatalities in a week. Using the Poisson model, what is the probability that this week it has 10 fatalities?
> A car dealership sells an average of 5 cars in a day. Using the Poisson model, what is the probability that the dealer sells 3 cars tomorrow?
> If this team has 200 corner kicks over the season, what are the chances that they score more than 22 times?
> In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
> A soccer team estimates that they will score on 8% of the corner kicks. In next week game, the team hopes to kick 15 corner kicks. What are the chances that they will score on 2 of those opportunities?
> A manufacturer ships toasters in cartons of 20. In each carton, they estimate a 5% chance that one of the toasters will need to be sent back for minor repairs. What is the probability that in a carton, there will be exactly 3 toasters that need repair?
> Do these situations involve Bernoulli trials? Explain. 1. You are rolling 5 dice and need to get at least two 6 to win the game. 2. We record the distribution of eye colors found in a group of 500 people. 3. A manufacturer recalls a doll because about 3%
> Suppose occurrences of sales on a small company website are well modeled by a Poisson model with λ=5/hour. 1. If a sale just occurred, what is the expected waiting time until the next sale? 2. What is the probability that the next sale will happen in th
> Below is a back-to-back stem-and-leaf display that shows two datasets at once one going to the left, one to the right. The display compares the percent change in population for two regions of the United States (based on census figures for 2000 and 2010).
> Lifetimes of electronic components can often be modeled by an Exponential model. Suppose quality control engineers want to model the lifetime of a hard drive to have a mean lifetime of 3 years. 1. What value of λ should they use? 2. With this model, wha
> In an effort to check the quality of their cell phones, a manufacturing manager decides to take a random sample of 10 cell phones from yesterday production run, which produced cell phones with serial numbers ranging (according to when they were produced)
> Do these situations involve Bernoulli trials? Explain. 1. We roll 50 dice to find the distribution of the number of spots on the faces. 2. How likely is it that in a group of 120 the majority may have Type A blood, given that Type A is found in 43% of th
> An automatic filling machine in a factory fills bottles of ketchup with a mean of 16.1 oz and a standard deviation of 0.05 oz with a distribution that can be well modeled by a Normal model. What is the probability that your bottle of ketchup contains les
> The life span of a calculator battery is Normally distributed with a mean of 45 hours and a standard deviation of 5 hours. What is the probability that a battery lasts more than 53 hours?
> A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of 11. Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviatio
> An employer pays a mean salary for a 5-day workweek of $1250 with a standard deviation of $129. On the weekends, his salary expenses have a mean of $450 with a standard deviation of $57. What is the mean and standard deviation of his total weekly salarie
> What is the standard deviation for Exercise 2 ?
> What is the standard deviation for Exercise 1 ?
> A coffee shop tracks sales and has observed the distribution in the following table. What is the average daily sales that it can expect?
> People with spinal cord injuries may lose function in some, but not all, of their muscles. The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs. Surgeons compared two
> A citrus farmer has observed the following distribution for the number of oranges per tree. How many oranges does he expect on average?
> Facebook reports that 70% of its users are from outside the United States and that 50% of its users log on to Facebook every day. Suppose that 20% of its users are U.S. users who log on every day. Make a probability table. Why is a table better than a tr
> If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.
> On the Titanic, the probability of survival was 0.323. Among first-class passengers, it was 0.625. Were survival and ticket class independent? Explain.
> A nervous kicker usually makes 70% of his first field goal attempts. If he makes his first attempt, his success rate rises to 90%. What is the probability that he makes his first two kicks?
> A student figures that he has a 30% chance of being let out of class late. If he leaves class late, there is a 45% chance that he will miss his train. What is the probability that it will cause him to miss the train?
> From Exercise 3, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?
> What is the probability that a person likes to watch football, given that she also likes to watch basketball?
> Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both?
> Given the probabilities in Exercise 12, what is the probability that a person is younger than 50 given that she uses online banking? Has the probability that she is younger than 50 increased or decreased with the additional information?
