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Statistical Reasoning For Everyday Life 4th Edition Jeff Bennett, Bill Briggs, Mario F. Triola - Solutions
Some studies have shown that, for certain ethnic groups, the incidence of melanoma (the most dangerous form of skin cancer) increases as latitude decreases. State the correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause or a direct
Consider the scatterplot in Figure 7.15.a. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points.b. Now include the outlier. How does the outlier affect the correlation coefficient? Estimate or compute the correlation coefficient
Consider the scatterplot in Figure 7.16.a. Which point is an outlier? Ignoring the outlier, estimate or compute the correlation coefficient for the remaining points. b. Now include the outlier. How does the outlier affect the correlation coefficient? Estimate or compute the correlation coefficient
The following table gives measurements of weight and shoe size for 10 people (including both men and women).a. Construct a scatterplot for the data. Estimate or compute the correlation coefficient. Based on this correlation coefficient, would you conclude that January and July temperatures are
An article in the New York Times on infant deaths included a statement that, based on the study results, putting infants to sleep in the supine position decreased deaths due to SIDS (sudden infant death syndrome). What is wrong with that statement?
The following table shows the average January high temperature and the average July high temperature for 10 major cities around the world.a. Construct a scatterplot for the data. Estimate or compute the correlation coefficient. Based on this correlation coefficient, would you conclude that January
Figure 7.17 shows the birth and death rates for different countries, measured in births and deaths per 1,000 population.a. Estimate the correlation coefficient and discuss whether there is a strong correlation between the variables. b. Notice that there appear to be two groups of data points within
The following (hypothetical) data set gives the number of hours 10 sixth-graders read per week and their performance on a standardized verbal test (maximum of 100).a) Construct a scatterplot for these data. Estimate or compute the correlation coefficient. Based on this correlation coefficient,
When studying salaries paid to CEOs of large companies, it is found that almost all of them range from a few hundred thousand dollars to several million dollars, but one CEO is paid a salary of $1. Is that salary of $1 an outlier? In general, how might outliers affect conclusions about correlation?
Does a scatterplot reveal anything about a cause and effect relationship between two variables?
If we have 20 pairs of sample data with a correlation coefficient of 1, then we know that one of the two variables is definitely the cause of the other. Decide whether the statement make sense or not? Explain clearly.
In one state, the number of unregistered handguns steadily increased over the past several years, and the crime rate increased as well. State the correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause or a direct cause? Explain your
What is a best-fit line (also called a regression line)? How is a best-fit line useful?
Use the scatterplot for life expectancy and infant mortality in Figure 7.4.a. Insert a best-fit line in the given scatterplot.b. Estimate or compute r and r2. Based on your value for r2, determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss
Use the scatterplot for number of farms and size of farms in Figure 7.5.a. Insert a best-fit line in the given scatterplot.b. Estimate or compute r and r2. Based on your value for r2, determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss
Use both scatterplots for actual and predicted temperature in Figure 7.6.a. Insert a best-fit line in the given scatterplot.b. Estimate or compute r and r2. Based on your value for r2, determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss
Use the data in Exercise 19 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
Use the data in Exercise 20 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
Use the data in Exercise 21 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
Use the data in Exercise 22 of Section 7.1. a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye. b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
Use the data in Exercise 23 of Section 7.1. To locate the points, use the midpoint of each income category; use a value of $25,000 for the category "less than $30,000," and use a value of $70,000 for the category "more than $60,000."a. Construct a scatterplot and, based on visual inspection, draw
Use the data in Exercise 24 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
Use the data in Exercise 25 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
For a study involving paired sample data, it is found that r = —0.4. What is the value of r2? In general, what is r2 called, what does it measure, and how can it be interpreted? That is, what does its value tell us about the variables?
Use the data in Exercise 26 of Section 7.1.a. Construct a scatterplot and, based on visual inspection, draw the best-fit line by eye.b. Briefly discuss the strength of the correlation. Estimate or compute r and r2. Based on your value for r2, identify how much of the variation in the variable can
An investigator has data consisting of heights of daughters and the heights of the corresponding mothers and fathers. She wants to analyze the data to see the effect that the height of the mother and the height of the father has on the height of the daughter. Should she use a (linear) regression or
R2. Using data described in Exercise 3, it is found that R2 = 0.68. Interpret that value. That is, what does that value tell us about the data?
A value of r2 = 1 is obtained from a sample of paired data with one variable representing the amount of gas (gallons) purchased and the total cost of the gas.
Using data from the National Health Survey, the equation of the best-fit line for women's heights and weights is obtained, and it shows that a woman 120 inches tall is predicted to weigh 430 pounds.
Using paired sample data consisting of the duration time (in seconds) of eruptions of Old Faithful geyser and the time interval (in minutes) after the eruption, a value of r2 = 0.926 is calculated, indicating that about 93% of the variation in the interval after eruption can be explained by the
Use the scatterplot for color and price in Figure 7.2.a. Insert a best-fit line in the given scatterplot.b. Estimate or compute r and r2. Based on your value for r2, determine how much of the variation in the variable can be accounted for by the best-fit line.c. Briefly discuss whether you could
Identify three different explanations for the presence of a correlation between two variables.
Heart disease can be cured by wearing a magnetic bracelet on your wrist. Determine whether the stated causal connection is valid. If the causal connection appears to be valid, provide an explanation.
Drinking greater amounts of alcohol decreases a person's reaction time. Determine whether the stated causal connection is valid. If the causal connection appears to be valid, provide an explanation.
You are trying to identify the cause of late-after moon headaches that plague you several days each week. For each of the following tests and observations, explain which of the six guidelines for establishing causality you used and what you concluded. Then summarize your overall conclusion based on
A famous study in Forum on Medicine concluded that the mean lifetime of conductors of major orchestras was 73.4 years, about 5 years longer than that of all American males at the time. The author claimed that a life of music causes a longer life. Evaluate the claim of causality and propose other
A study reported in Nature claims that women who give birth later in life tend to live longer. Of the 78 women who were at least 100 years old at the time of the study, 19% had given birth after their 40th birthday. Of the 54 women who were 73 years old at the time of the study, only 5.5% had given
Suppose that people living near a high-voltage power line have a higher incidence of cancer than people living farther from the power line. Can you conclude that the high-voltage power line is the cause of the elevated cancer rate? If not, what other explanations might there be for it? What other
In theory, we can use experiments to rale out two of the three different explanations for the presence of a correlation between two variables. Which of the three explanations do we not want to rale out? Why would we not want to rule it out?
What is a confounding variable? How can a confounding variable create a situation in which an underlying causality is hidden?
What is the difference between finding a correlation between two variables and establishing causality between two variables?
In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns.a. What single value is the best estimate of the population proportion of all adults who say that it is morally wrong to not report all income on tax returns?b.
We want to estimate the mean IQ score on the Stanford-Binet test for the population of college students. We know that for people randomly selected from the general population, the standard deviation of IQ scores on the Stanford-Binet test is 16.a. Using a standard deviation of 16, how many college
A sample of 40 randomly selected women is obtained, and the blood platelet count of each subject is measured. The mean is 279.5 and the standard deviation is 65.2.a. Use these sample results to construct a 95% confidence interval estimate of the population mean.b. What is the margin of error?c.
(a) You have been hired by Intel to determine the proportion of computer owners who plan to upgrade to a new operating system. Assuming that you want to be 95% confident that your sample proportion is within 0.02 of the true population proportion, how many people must you survey?(b) Suppose that,
When 40 women were randomly selected and tested for their cholesterol levels, a mean of 240.9 milligrams was obtained. Would you be more confident of your estimate if the sample included measurements from 500 women? Explain.
Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 ounces. A random sample of 36 cans has a mean amount of 12.19 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 12.00 ounces, and those sample means have a standard deviation of
Assume that the population of heights of men has a normal distribution with a mean of 69.5 in. and random samples of 100 men result in sample mean heights with a mean of 69.5 in. and a standard deviation of 0.24 in. a. If one sample of 100 men results in a mean height of 69.0 in., how many standard
Suppose that, in a suburb of 12,345 people, 6,523 people moved there within the past five years. You survey 500 people and find that 245 of the people in your sample moved to the suburb in the past five years. a. What is the population proportion of people who moved to the suburb in the past five
The College of Portland has 2,444 students and 269 of them are left-handed. You conduct a survey of 50 students and find that 8 of them are left-handed. a. What is the population proportion of left-handed students? b. What is the sample proportion of left-handed students? c. If the sample mean
You select a random sample of 150 people at a medical convention attended by 1,608 people. Within your sample, you find that 73 people have traveled from abroad. Based on this sample statistic, estimate how many people at the convention traveled from abroad. Would you be more confident of your
A random sample of 500 people was selected from the 103,219 people in attendance at the Super Bowl game between the Green Bay Packers and the Pittsburgh Steelers. Within the sample, 290 people supported the Packers. Based on this result, estimate how many people at the game supported the Packers.
Suppose you know that the distribution of sample proportions of nonresidents in samples of 200 students is normal with a mean of 0.34 and a standard deviation of 0.03. Suppose you select a random sample of 200 students and find that the proportion of nonresident students in the sample is 0.32.a.
Suppose you know that the distribution of sample proportions of women employees is normal with a mean of 0.42 and a standard deviation of 0.21. Suppose you select a random sample of employees and find that the proportion of women in the sample is 0.45. a. How many standard deviations is the sample
A quarterback threw 1 interception in his first game, 2 interceptions in his second game, 5 interceptions in his third game, and then he retired. Consider the values of 1, 2, and 5 to be a population. Assume that samples of size 2 are randomly selected (with replacement) from the population.a. List
America Online published a survey question. Among the 2,300 Internet users who responded, 20% answered "yes" and the others answered "no." For the "yes" responses, what is the value of /5? What is fundamentally wrong with this survey?
Here is the population of all five U.S. presidents who had professions in the military, along with their ages at inauguration: Eisenhower, 62; Grant, 46; Harrison, 68; Taylor, 64; and Washington, 57. Assume that samples of size 2 are randomly selected (with replacement) from the population of five
Three states and their areas (in thousands of square miles) are given in the following table. Consider these three states to be the entire population from which samples of size n = 2 will be selected (with replacement).a. Find the mean of each of the 9 different possible samples.b. What is the mean
The ages (years) of the four U.S. presidents when they were assassinated in office are 56 (Lincoln), 49 (Garfield), 58 (McKinley), and 46 (Kennedy). Consider these four ages to be a population.a. Assuming that two of the ages are randomly selected to form samples of size n = 2 with replacement,
What does x denote, what does p, denote, and what is the difference between them?
Two different surveys will be conducted to estimate the mean salary of employees who have taken a statistics course. If the first survey has a larger sample size than the second survey, the first survey will result in a sample mean that is closer to the population mean (when compared with the
A researcher for a car dealership wants to estimate the mean age of cars in his county. He goes to the largest shopping mall, he randomly selects 3,000 cars in the parking lot, and he obtains their ages from the registration stickers on the car window*. He then computes the mean age of the sample
In an Adecco Staffing survey of 1,000 adults in the United States, 140 (or 14%) said that salary was the most important feature of their job. The sample proportion of 0.14 cannot be a good estimate of the population proportion because this survey is based on such a small proportion of the
In a survey of children 5 to 17 years old, 1,050 children were randomly selected from the nine states in the Northeast, and the proportion who spoke a language other than English in their home was 0.19. Is that sample proportion a good estimate for children in the United States? Why or why not?
From a random sample of weights of dollar coins, we construct this 95% confidence interval estimate of the mean: 8.0518 grams < u < 8.0902 grams Interpret this confidence interval.
Exercises 10, assume that population means are to be estimated from the samples described. In each case, use the sample results to approximate the margin of error and 95% confidence interval.Sample size = 81, sample mean = 4.5 km, sample standard deviation = 3.1 km
Exercises 11, assume that population means are to be estimated from the samples described. In each case, use the sample results to approximate the margin of error and 95% confidence interval.n = 100, x = 8.0 ft, s = 2.0 ft
Exercises 12, assume that population means are to be estimated from the samples described. In each case, use the sample results to approximate the margin of error and 95% confidence interval.n = 64, x = $550, s = $60
For Exercises 14, assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given.Margin of error = 18.2 cm, standard
For Exercises 15, assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given.Margin of error = 3.5 ml, standard
For Exercises 16, assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given.Margin of error = 0.5 g, standard
Nielsen Media Research wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.25 hour is desired. Past studies suggest that a population standard deviation of 1.7 hours is reasonable. Estimate the minimum sample size required to
A government survey conducted to estimate the mean price of houses in a large metropolitan area is designed to have a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $65,500. Estimate the minimum sample size needed to estimate the population mean with the
An economist wants to estimate mean annual income from the first year of work for college graduates who have had the profound wisdom to take a statistics course. How many such incomes must be found if she wants to be 95% confident that the sample mean is within $750 of the true population mean?
You want to estimate the mean weight of quarters in circulation. A sample of 40 quarters has a mean weight of 5.639 grams and a standard deviation of 0.062 gram. Use a single value to estimate the mean weight of all quarters. Also, find the 95% confidence interval.
A sample of 186 newborn babies has a mean weight of 3103 g and a standard deviation of 696 g. Use a single value to estimate the mean weight of a new-born baby. Also, find the 95% confidence interval.
Data from the National Center for Education Statistics on 4,400 college graduates show that the mean time required to graduate with a bachelor's degree is 5.15 years with a standard deviation of 1.68 years. Use a single value to estimate the mean time required to graduate for all college graduates.
Based on a sample of 62 households, the mean weight of discarded plastic is 1.91 pounds and the standard deviation is 1.07 pounds (data from the Garbage Project at the University of Arizona). Use a single value to estimate the mean weight of discarded plastic for all households. Also, find the 95%
The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of the weights (pounds) of such bears is given below. Find a 95% confidence interval estimate of the mean of the population of all such bear weights.
When people smoke, the nicotine they absorb is converted to cotinine, which can be measured. A sample of cotinine levels of 40 smokers is listed below. Find a 95% confidence interval estimate of the mean cotinine level of all smokers.
You select a random sample of n = 31 families in your neighborhood and find the following family sizes (number of people in the family):a. What is the mean family size for the sample?b. What is the standard deviation for the sample?c. What is the best estimate for the mean family size for the
A random sample of n = 31 households is asked the number of TV sets in the household. The responses are as follows:a. What is the mean number of TVs for the sample?b. What is the standard deviation for the sample?c. What is the best estimate for the mean number of TVs for the population of all
Here is a typical statement made by the media: "Based on a recent study, pennies weigh an average of 2.5 grams with a margin of error of 0.006 gram." What important and relevant piece of information is omitted from that statement? Is it OK to use the word "average"?
The National Health Examination involves measurements from about 25,000 people, and the results are used to estimate values of various population means. Is it valid to criticize this survey because the sample size is only about 0.01% of the population of all Americans? Explain.
The mean income of high school mathematics teachers was estimated to be $48,213 with a margin of error of five percentage points.
When sample data were used to estimate the value of the mean weight of all pennies, this 95% confidence interval was obtained: 2.512 grams < /x < 2.512 grams Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Exercises 9, assume that population means are to be estimated from the samples described. In each case, use the sample results to approximate the margin of error and 95% confidence interval.Sample size = 49, sample mean = 25.2 cm, sample standard deviation = 2.2 cm
In an Accountemps survey, senior executives were asked to identify the most common error made in interviews of job applicants. The following 95% confidence interval estimates the population proportion p for "little or no knowledge of the company." Interpret that confidence interval. 0.393 < p <
Sample size = 800, sample proportion = 0.25Assume that population proportions are to be estimated from the samples described. In each case, find the approximate margin of error and 95% confidence interval.
n = 550, p = 0.1Assume that population proportions are to be estimated from the samples described. In each case, find the approximate margin of error and 95% confidence interval.
n = 780, p = 0.160Assume that population proportions are to be estimated from the samples described. In each case, find the approximate margin of error and 95% confidence interval.
E = 0.015Estimate the minimum sample size needed to achieve the given margin of error.
E = 0.035 Estimate the minimum sample size needed to achieve the given margin of error.
Nielsen Media Research uses samples of 5,000 households to rank TV shows. Nielsen reported that 60 Minutes had 15% of the TV audience. What is the 95% confidence interval for this result?
Repeat Exercise 17 assuming that the sample size is doubled to 10,000. Given that the large cost and effort of conducting the Nielsen survey would be doubled, does this increase in sample size appear to be justified by the increased reliability?
A study done by researchers at Alfred University concluded that 80% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1,400 athletes. What are the margin of error and 95% confidence interval for the study?
In a study of 1,228 randomly selected medical malpractice lawsuits, it is found that the proportion that were dropped or dismissed is 0.697. When a 95% confidence interval is constructed for the population proportion of all lawsuits, the margin of error is found to be 0.026. Identify the confidence
An annual survey of first-year college students, conducted by the Higher Education Research Institute at UCLA, asks approximately 276,000 students about their attitudes on a variety of subjects. According to a recent survey, 51% of first-year students believe that abortion should be legal (down
The Genetics and IVF Institute conducted clinical trials of the YSORT method designed to increase the probability of conceiving a boy. Among 152 babies born to parents using the YSORT method, 127 were boys. Identify the margin of error and the 95% confidence interval for these clinical trials.
A Pew Research Center poll included 1708 randomly selected adults who were asked whether "global warming is a problem that requires immediate government action." Results showed that 939 of those surveyed indicated that immediate government action is required. A news reporter wants to determine
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