Statistical Reasoning For Everyday Life 4th International Edition Jeffrey Bennett, William L. Briggs, Mario F. Triola - Solutions

Find last season’s NFL team statistics. Construct a table showing the following for each team: number of wins, average yards gained on offense per game, and average yards allowed on defense per game. Make scatterplots to explore the correlations between offense and wins and between defense and
Select a sample of at least eight people and measure each person’s height and arm span. (When you measure arm span, the person should stand with arms extended like the wings on an airplane.) Using the paired sample data, construct a scatterplot and estimate or calculate the value of the
Select a sample of at least eight people and record each person’s pulse rate by counting the number of heartbeats in 1 minute. Also record each person’s height. Using the paired sample data, construct a scatterplot and estimate or calculate the value of the correlation coefficient. What do you
Find a recent news report that discusses some type of correlation. Describe the correlation. Does the article give any sense of the strength of the correlation? Does it suggest that the correlation reflects any underlying causality? Briefly discuss whether you believe the implications the article
Give examples of two variables that you expect to be positively correlated. Explain why the variables are correlated and why the correlation is (or is not) important.
A set of paired sample data results in a correlation coefficient of r = 0, so the scatterplot will show that there is no pattern of the plotted points.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly;
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.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly;
If we conduct a study showing that there is a strong negative correlation between resting pulse rate and amounts of time spent in rigorous exercise, we can conclude decreases in resting pulse rates are somehow associated with increases in exercise.For Exercises 5–8, decide whether the statement
If we have two variables with one being the direct cause of the other, then there may or may not be a correlation between those two variables.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of
Statistics students find that as they spend more time studying, their test scores are higher.Exercises 9–16 make statements about a correlation. In each case, state the correlation clearly. (For example, we might state that “there is a positive correlation between variable A and variable
Astronomers have discovered that, with the exception of a few nearby galaxies, all galaxies in the universe are moving away from us. Moreover, the farther the galaxy, the faster it is moving away. That is, the more distant a galaxy, the greater the speed at which it is moving away from us.Exercises
Find data for recent years concerning the Super Bowl winner and the end-of-year change in the stock market (positive or negative). Do recent results still agree with the correlation? Explain.
a. Describe a real situation in which there is a positive correlation that is the result of coincidence.b. Describe a real situation in which there is a positive correlation that is the result of a common underlying cause.c. Describe a real situation in which there is a positive correlation that
r2 Value. 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.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).
r2 Value. A value of r2 = -0.040 is obtained from a sample of men, with each pair of data consisting of the height in inches and the SAT score for one man.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
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.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make
Use the scatterplot for color and price in Figure 2.For Exercises 9–12, do the following.
Use the data in Exercise 19 of Section 1.Exercises 13–20 refer to the tables in the Section 1 Exercises. In each case, do the following.
Use the data in Exercise 21 of Section 1.Exercises 13–20 refer to the tables in the Section 1 Exercises. In each case, do the following.
Use the data in Exercise 23 of Section 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$.”Exercises 13–20 refer to the tables in the
Use the data in Exercise 25 of Section 1 Exercises 13–20 refer to the tables in the Section 1 Exercises. In each case, do the following.
The following table gives five population indicators for eleven selected countries. Study these data and try to identify possible correlations. Doing additional research if necessary, discuss the possible correlations you have found, speculate on the reasons for the correlations, and discuss
Figure 4 shows two distributions: (a) a famous data set of the chest sizes of 5,738 Scottish militiamen collected in about 1846 and (b) the distribution of the population densities of the 50 states. Is either distribution a normal distribution? Explain. Figure 4 Frequency 1,200 1,000 12 10 800 600
Look again at the normal distribution in Figure 5.a. Estimate the percentage of births occurring between 0 and 60 days after the due date.b. Estimate the percentage of births occurring between 14 days before and 14 days after the due date. This region has about 18% of the total area under the
Which of the following variables would you expect to have a normal or nearly normal distribution?a. Scores on a very easy testb. Shoe sizes of a random sample of adult womenc. The number of apples in each of 100 full bushel baskets.
The tests that make up the verbal (critical reading) and mathematics parts of the SAT (and the GRE, LSAT, and GMAT) are designed so that their scores are normally distributed with a mean of m = 500 and a standard deviation of s = 100. Interpret this statement.
Vending machines can be adjusted to reject coins above and below certain weights. The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.0700 gram. If a vending machine is adjusted to reject quarters that weigh more than 5.81 grams and
Consider again the question of whether you should advise a pregnant friend to schedule an important business meeting 2 weeks before her due date. Actual data suggest that the number of days between the birth date and the due date is normally distributed with a mean of m = 0 days and a standard
You measure your resting heart rate at noon every day for a year and record the data. You discover that the data have a normal distribution with a mean of 66 and a standard deviation of 4.On how many days was your heart rate below 58 beats per minute?
The Stanford-Binet IQ test is scaled so that scores have a mean of 100 and a standard deviation of 16. Find the standard scores for IQs of 85, 100, and 125.
Cholesterol levels in men 18 to 24 years of age are normally distributed with a mean of 178 and a standard deviation of 41.a. What is the percentile for a 20-year-old man with a cholesterol level of 190?b. What cholesterol level corresponds to the 90th percentile, the level at which treatment may
IQ scores are normally distributed with a mean of 100 and a standard deviation of 16. What are the IQ scores for people in the 75th and 40th percentiles on IQ tests?
The heights of American women ages 18 to 24 are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. In order to serve in the U.S. Army, women must be between 58 inches and 80 inches tall. What percentage of women are ineligible to serve based on their height?
You are a middle school principal and your 100 eighth-graders are about to take a national standardized test. The test is designed so that the mean score is m = 400 with a standard deviation of s = 70. Assume the scores are normally distributed.a. What is the likelihood that one of your
The mean salary of the 9,000 employees at Holley Inc. is m = +26,400 with a standard deviation of s = +2,420. A pollster samples 400 randomly selected employees and finds that the mean salary of the sample is $26,650. Is it likely that the pollster would get these results by chance, or does the
The rate of unemployment has statistical significance because it has such a strong effect on the economy.For Exercises 5–8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so
In an experiment testing a method of gender selection, 1,000 couples give birth to 550 girls and 450 boys. Because the probability of getting such extreme results by chance is only 0.0009, the results are statistically significant.For Exercises 5–8, decide whether the statement makes sense (or is
In a test of a technique of gender selection, the 100 babies born consist of at least 80 girls. Because there is about 1 chance in a billion of getting at least 80 girls among 100 babies, the results are statistically significant.For Exercises 5–8, decide whether the statement makes sense (or is
In a survey, 50 students are randomly selected among all college students currently taking a statistics course, and it is found that they are all females.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is
In a pre-election survey, 100 likely voters are randomly selected from adults in the United States, and it is found that 6% of them are Democrats.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is statistically
In 6 rolls of a six-sided die, the outcome of 6 never occurs.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is statistically significant. Discuss any implications of the statistical significance.
A common lottery game is to select four digits, each between 0 and 9 (inclusive). Winning requires that you get the same four digits that are drawn, and they must be in the same order. You select four digits for one ticket, and none of your selections matches the numbers drawn.For each event in
In conducting a survey of adults in the United States, a pollster claims that he randomly selected 20 subjects and all of them were women.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is statistically significant.
A commuter enters a New York City subway car near Times Square and finds that it is occupied by 50 men, all of whom are bald.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is statistically significant. Discuss any
For a trial on a charge of failure to pay child support, the jury consists of exactly 6 men and 6 women.For each event in Exercises 9–16, state whether the difference between what occurred and what you would have expected by chance is statistically significant. Discuss any implications of the
In a clinical trial of a new drug intended to treat allergies, 5 of the 80 subjects in the treatment group experienced headaches, and 8 of the 160 subjects in the control group experienced headaches.For each event in Exercises 9–16, state whether the difference between what occurred and what you
A study of 75 students who took an SAT preparation course (American Education Research Journal, Vol. 19, No. 3) concluded that the mean improvement on the SAT was 0.6 point. If we assume that the preparation course has no effect, the probability of getting a mean improvement of 0.6 point by chance
A National Health Survey determined that the mean weight of a sample of 804 men ages 25 to 34 years was 176 pounds, while the mean weight of a sample of 1,657 men ages 65 to 74 years was 164 pounds. The difference is significant at the 0.01 level. Interpret this result.
The cumulative frequency of a category in a table is 25.5.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The registered voters of Rochester County are 25% Democrats, 25% Republicans, and 50% independents. Construct a pie chart to represent the party affiliations. Registered Voters in Rochester County Republican 25% Democrat 25% Independent 50%
Many states have lotteries that involve the random selection of digits 0, 1, 2, …,
Is the distribution of those digits a normal distribution? Why or why not?
Birth weights in the United States are normally distributed with a mean (in grams) of 3420 g and a standard deviation of 495 g. If you graph this normal distribution, the area to the right of 4000 g is 0.12. What is the area to the left of 4000 g?
A sample of 2,000 women is randomly selected, and it is found that the heights of the women are normally distributed with a mean of 63.6 in.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
As part of a study of the relationship between brain size and IQ, a random sample of 250 adult males is obtained and their brain volumes are measured and found to be normally distributed.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).
An economist plans to obtain the current salaries of all professional football players, and she predicts that those salaries will have a normal distribution.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The numbers selected in the Pennsylvania “Match 6” lottery, in which players attempt to match six randomly selected numbers between 1 and 49.State whether you would expect it to be normally distributed. Explain your reasoning.
The lengths of time that commercial aircraft are delayed before departing.State whether you would expect it to be normally distributed. Explain your reasoning.
The waiting times at a bus stop if the bus comes once every 10 minutes and you arrive at random times.State whether you would expect it to be normally distributed. Explain your reasoning.
Figure 9 shows a histogram for the pulse rates of 98 students. The mean pulse rate is 71.2 beats per minute. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 9 Frequency 60 60 40 20 -20 0 20 40 60 80 100 120 Heart rate (beats per minute)
Figure 10 shows a histogram for the weights of 50 randomly selected quarters. The mean weight is 5.62 grams. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 10 20 20 Frequency 15 10 10 5 0 5.4 5.5 5.6 5.7 5.8 5.9 Weight of quarters
Consider the graph of the normal distribution in Figure 14, which illustrates the relative frequencies in a distribution of systolic blood pressures for a sample of female students. The distribution has a standard deviation of 14.a. What is the mean of the distribution?b. Estimate (using area) the
Using the guidelines given in the text, choose a variable that you think should be nearly normally distributed. Collect at least 30 data values for the variable and make a histogram. Comment on how closely the distribution fits a normal distribution. In what ways does it differ from a normal
Men’s heights are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in. What is the standard z-score for a man with a height of 69.0 in.?
The standard score for the height of a male is z = -2. Is the height of this male above or below the mean height of all males? How many standard deviations away from the mean is this?
For rolling a die, the mean outcome is 3.5. Can we apply the 68-95-99.7 rule and conclude that 95% of all outcomes fall within 2 standard deviations of 3.5? Why or why not?
Birth weights (in grams) in Lichtenstein are normally distributed with a mean of 3,420 g and a standard deviation of 0 g.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Scores on a standard test of depth perception are normally distributed with two different modes.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Percentage of scores greater than 148 Use the normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 16. Use Table 1 to find the indicated quantities. Note: Table 1 shows standard scores from -3.5 to +3.5. In these problems, for standard scores above 3.5, use a
Percentage of scores between 76 and 108 Table 1 to find the indicated quantities. Note: Table 1 shows standard scores from -3.5 to +3.5. In these problems, for standard scores above 3.5, use a percentile of 99.99%; for all standard scores below -3.5, use a percentile of 0.01%.Use the normal
The percentage of heights greater than 162 centimeters
The percentage of heights less than 168 centimeters
The percentage of heights greater than 156 centimeters
The percentage of heights greater than 171 centimeters
The percentage of heights less than 177 centimeters
The percentage of heights less than 147 centimeters
The percentage of heights less than 144 centimeters
The percentage of heights greater than 179 centimeters
The percentage of heights between 156 centimeters and 168 centimeters
The percentage of heights between 159 centimeters and 165 centimeters
The percentage of heights between 148 centimeters and 170 centimeters
The percentage of heights between 146 centimeters and 156 centimeters
In this section, it was noted that the standard deviation of sample means is s/1n. In that expression, what does s represent and what does n represent?
The population of unemployed adults has ages with mean m and standard deviations. Samples of unemployed adults are randomly selected so that there are exactly 100 in each sample. For each sample, the mean age is computed. What does the Central Limit Theorem tell us about the distribution of those
In the United States, there are many people with little or no accumulated wealth, and there are a few people with very large amounts of wealth. What does this suggest about the symmetry of the distribution of wealth?
When the digits 0 through 9 are selected for a state lottery, the digits are selected in a way that they are all equally likely. Which term best describes the distribution of selected digits: skewed, bimodal, uniform, or unimodal?
What is skewness in a graph?
Because a data set has three modes, it must have a skewed distribution.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Examination of the data set reveals that it is symmetric with a mean of 98.2 and a median of 98.2.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Examination of a data set reveals that its distribution is left-skewed and unimodal.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Examination of a data set reveals that the mean and median are both equal to 98.2, so the distribution must be uniform.Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
The histogram in Figure 9 shows the times between eruptions of Old Faithful geyser in Yellowstone National Park for a sample of 300 eruptions (with 299 times between eruptions). Over the histogram, draw a smooth curve that captures its general features. Then classify the distribution according to
The histogram in Figure 10 shows the time until failure for a sample of 108 computer chips. Over the histogram, draw a smooth curve that captures its general features. Then classify the distribution according to its number of modes and its symmetry or skewness. In words, summarize the meaning of
The histogram in Figure 11 shows the weights of a sample of 391 rugby players. Over the histogram, draw a smooth curve that captures its general features. Then classify the distribution according to its number of modes and its symmetry or skewness. In words, summarize the meaning of your results.
In a recent year, the 817 professional baseball players had salaries with the following characteristics: • The mean was $$3,250,178$. • The median was $$1,152,000$. • The salaries ranged from a low of $$400,000$ to a high of $$33,000,000$. a. Describe the shape of the
The heights of 500 male students, half of whom are adults while the other half are eight years of age.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
The weights of the cola in 1000 randomly selected cans of Coke.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
The weights of cars in a fleet consisting of 50 compact cars and 50 delivery trucks.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?
The ages of 1,000 randomly selected patients being treated for dementia.Answer the following questions: a. How many modes would you expect for the distribution? b. Would you expect the distribution to be symmetric, left-skewed, or right-skewed?

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Statistical Reasoning For Everyday Life 4th International Edition Jeffrey Bennett, William L. Briggs, Mario F. Triola - Solutions

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