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statistics
elementary statistics a step by step approach
Questions and Answers of
Elementary Statistics A Step By Step Approach
Find the \(P\)-value when the \(t\) test statistic is 2.983 , the sample size is 6 , and the test is two-tailed.
A physician claims that joggers' maximal volume oxygen uptake is greater than the average of all adults. A random sample of 15 joggers has a mean of 40.6 milliliters per kilogram \((\mathrm{ml} /
A researcher claims, based on information obtained from the Harper's Index, that \(23 \%\) of Americans say that they dream in black and white. To test the claim, the researcher randomly selected 100
A report stated that \(31.9 \%\) of babies are delivered by Caesarean section. A researcher believes that the percentage is less than \(31.9 \%\) in a large hospital. The researcher randomly selected
A statistician read that at least \(77 \%\) of the population oppose replacing \(\$ 1\) bills with \(\$ 1\) coins. To see if this claim is valid, the statistician selected a random sample of 80
An attorney claims that more than \(25 \%\) of all lawyers advertise. A random sample of 200 lawyers in a certain city showed that 63 had used some form of advertising. At \(\alpha=0.05\), is there
Find the critical chi-square value for 15 degrees of freedom when \(\alpha=0.05\) and the test is right-tailed.
Find the critical chi-square value for 10 degrees of freedom when \(\alpha=0.05\) and the test is left-tailed.
Find the critical chi-square values for 22 degrees of freedom when \(\alpha=0.05\) and a two tailed test is conducted.
A psychologist wishes to see if the variance in IQ of 10 counseling patients is less than the variance of the population, which is 225 . The variance of the IQs of the 10 patients was 206 . Test her
A hospital administrator believes that the standard deviation of the number of people using outpatient surgery per day is greater than 8 . A random sample of 15 days is selected. The data are shown.
A cigarette manufacturer wishes to test the claim that the variance of the nicotine content of its cigarettes is 0.644 . Nicotine content is measured in milligrams, and assume that it is normally
Find the \(P\)-value when \(\chi^{2}=19.274, n=8\), and the test is right-tailed.
Find the \(P\)-value when \(\chi^{2}=3.823, n=13\), and the test is left-tailed.
A researcher knows from past studies that the standard deviation of the time it takes to inspect a car is 16.8 minutes. A random sample of 24 cars is selected and inspected. The standard deviation is
A researcher read that the average amount of money stolen in a bank robbery is \(\$ 4330\). The researcher randomly selected 50 recent successful bank robberies and found that the average amount of
A researcher claims that adult hogs fed a special diet will have an average weight of 200 pounds. A random sample of 10 hogs has an average weight of 198.2 pounds and a standard deviation of 3.3
The Incredible Edible Egg company recently found that eating eggs does not increase a person’s blood serum cholesterol. Five hundred subjects participated in a study that lasted for 2 years. The
You recently received a job with a company that manufactures an automobile antitheft device.To conduct an advertising campaign for the product, you need to make a claim about the number of automobile
A tobacco company claims that its best-selling cigarettes contain at most 40 mg of nicotine. This claim is tested at the 1% significance level by using the results of 15 randomly selected
Assume you are part of a research team that compares products designed to help people quit smoking.Condor Consumer Products Company would like more specific details about the study to be made
Assume that you are working for the Consumer Protection Agency and have recently been getting complaints about the highway gas mileage of the new Dodge Caravans. Chrysler Corporation agrees to allow
Hypothesis testing and testing claims with confidence intervals are two different approaches that lead to the same conclusion. In the following activities, you will compare and contrast those two
An adult has on average 5.2 liters of blood. Assume the variable is normally distributed and has a standard deviation of 0.3 . Find the percentage of people who have less than 5.4 liters of blood in
Each month, an American household generates an average of 28 pounds of recyclable paper waste. Assume the variable is approximately normally distributed and the standard deviation is 2 pounds. If a
The average weight of the human male brain is 3.08 pounds. Assume the variable is approximately normally distributed, and the population standard deviation is 0.3 pounds. If 50 males are randomly
To qualify for a police academy, candidates must score in the top \(10 \%\) on a general abilities test. Assume the test scores are normally distributed and the test has a mean of 200 and a standard
For a medical study, a researcher wishes to select people in the middle \(60 \%\) of the population based on blood pressure. Assuming that blood pressure readings are normally distributed and the
A survey of 18 high-tech firms showed the number of days' inventory they had on hand. Determine if the data are approximately normally distributed. 5 29 34 44 45 63 68 74 74 81 88 91 97 98 113 118
The data shown consist of the number of games played each year in the career of Baseball Hall of Famer Bill Mazeroski. Determine if the data are approximately normally distributed. 81 148 152 135 151
A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3
A recent study found that an American skips breakfast on average 50 times a year. Assume the standard deviation is 4. If a random sample of 36 Americans is selected, find the probability that the
The average time spent by construction workers who work on weekends is 7.93 hours (over 2 days). Assume the distribution is approximately normal and has a standard deviation of 0.8 hour.a. Find the
It has been reported that last year \(25 \%\) of drivers have fallen asleep at the wheel. If 200 drivers are selected at random, find the probability that 62 will say that they have fallen asleep
Ten percent of Americans are allergic to ragweed. If a random sample of 200 people is selected, find the probability that 10 or more will be allergic to ragweed.
A recent survey found that \(40 \%\) of students in college change their major field at least once in their college careers. Find the probability that in a random sample of 100 college students, at
When \(n=10\) and \(p=0.5\), use the binomial distribution table (Table A-2 in Appendix A) to find the probability that \(X=6\). Then use the normal approximation to find the probability that \(X=6\).
Many times in statistics it is necessary to see if a set of data values is approximately normally distributed. There are special techniques that can be used. One technique is to draw a histogram for
Twenty students from a statistics class each collected a random sample of times on how long it took students to get to class from their homes. All the sample sizes were 30. The resulting means are
Assume one of your favorite activities is mountain climbing. When you go mountain climbing, you have several safety devices to keep you from falling. You notice that attached to one of your safety
Assume you are thinking about starting a Mensa chapter in your hometown, which has a population of about 10,000 people. You need to know how many people would qualify for Mensa, which requires an IQ
A researcher wishes to estimate the number of times a person skips breakfast during the year. A random sample of 49 people had a mean of 50. Assume the population standard deviation is 2.6. Find the
A nutritionist wanted to find the average amount of candy consumed per year by adult Americans. The nutritionist selected a random sample of 60 adults to study. The sample mean was 23.9 pounds of
The following data represent a random sample of the assets (in millions of dollars) of 30 credit unions in southwestern Pennsylvania. Assume the population standard deviation is 14.405 . Find the
A sociologist wishes to estimate the average number of automobile thefts in a large city per day within 2 automobiles. He wishes to be \(99 \%\) confident, and from a previous study the standard
Find the \(t_{\alpha / 2}\) value for a \(95 \%\) confidence interval when the sample size is 22 .
A random sample of 16 cats had a mean life expectancy of 15.3 years. The standard deviation of the sample was 2.3 years. Assume the variable is normally distributed. Find the \(95 \%\) confidence
The data represent a random sample of the number of home fires started by candles for the past several years. (Data are from the National Fire Protection Association.) Find the \(99 \%\) confidence
A random sample of 150 assault victims in a large city found that 45 took no selfprotection actions against the criminal. Find \(\hat{p}\) and \(\hat{q}\), where \(\hat{p}\) is the proportion of
A survey conducted by Sallie Mae and Gallup of 1404 respondents found that 323 students paid for their education by student loans. Find the \(90 \%\) confidence interval of the true proportion of
A survey of 6000 adults found that \(58 \%\) say that they would take a ride in a fully selfdriving car. Find the \(90 \%\) confidence interval of the true proportion who said that they would take a
A researcher wishes to estimate, with \(95 \%\) confidence, the proportion of people who did not have a land line phone. A previous study shows that \(40 \%\) of those interviewed did not have a land
assume that no previous study was done. Find the minimum sample size necessary to be accurate within \(2 \%\) of the true population.
Find the values for \(\chi_{\text {right }}^{2}\) and \(\chi_{\text {left }}^{2}\) for a \(90 \%\) confidence interval when \(n=25\).
A study of 30 automobile owners found that the standard deviation of the ages of their automobiles is 1.7 years. Find the \(95 \%\) confidence interval of the variance and standard deviation of the
Find the \(90 \%\) confidence interval for the variance and standard deviation for the number of named storms per year in the Atlantic basin. A random sample of 10 years has been used. Assume the
Shown are the ages (in years) of the Presidents at the times of their deaths.1. Do the data represent a population or a sample?2. Select a random sample of 12 ages and find the variance and standard
A researcher wishes to see if there is a difference between the dropout rate of students who attend two-year colleges and the dropout rate of students who attend four-year colleges. The researcher
Assume you get a new job as a coach for a sports team, and one of your first decisions is to choose the sports drink that the team will use during practices and games. You obtain a Sports Report
Assume you work for a corporation that makes facial tissues. The job you are presently working on requires you to decide how many tissues are to be put in the new automobile glove compartment boxes.
1. Do you feel that your population should be limited to a select group of workers such as government employees, hospital workers, teachers, fast-food workers, etc.?2. What type of sample would you
State the null and alternative hypotheses for each conjecture.a. A researcher thinks that the average amount of sugar consumed by an adult is less than 147 pounds per year.b. A researcher feels that
Using Table A-4 in Appendix A, find the critical value(s) for each situation and draw the appropriate figure, showing the critical region.a. A left-tailed test with \(\alpha=0.10\).b. A two-tailed
A researcher believes that the average number of hours a person spends in traffic each year is more than the national average of 46 (Texas Transportation Institute). Assume the population standard
For a specific year, the average score on the SAT Math test was 515.* The variable is normally distributed, and the population standard deviation is 100. A school superintendent wishes to see if her
Construct a probability distribution for rolling a single die.
Represent graphically the probability distribution for the sample space for tossing three coins. Number of heads X Probability P(X) 0 2 -1x 3
A company employs 25 salespeople. During a randomly selected week, 5 people made 2 sales, 11 people made 3 sales, 6 people made 4 sales, and 3 people made 5 sales. Construct a probability
Determine whether each distribution is a probability distribution. X 1 3 5 7 9 a. P(X) 0.4 0.2 0.1 0.3 0.1 X -$5 $0 $5 $10 b. P(X) AP
Find the mean of the number of spots that appear when a die is tossed.
A very old water system in a manufacturing plant has 4 independent valves that have a \(50 \%\) chance of working correctly over a year. The valves are checked yearly to make sure a valve is either
If three coins are tossed, find the mean of the number of heads that occur.
Find the mean for the number of successful sales per person per week.
Compute the variance and standard deviation for the probability distribution.
A box contains 5 balls. Two are numbered 3, one is numbered 4, and two are numbered 5 . The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is
On a randomly selected day, 25 people were found guilty of illegally selling various drugs. Nine had no prior sentences. Six had one prior sentence. Five had two prior sentences. Three had three
One thousand tickets are sold at \(\$ 1\) each for a smart television valued at \(\$ 750\). What is the expected value of the gain if you purchase one ticket?
Poker chips are numbered \(\$ 1, \$ 5, \$ 10, \$ 20\), and \(\$ 50\). Four chips are numbered \(\$ 1\). Two chips are numbered \(\$ 5\). Two chips are numbered \(\$ 10\). One chip is numbered \(\$
A financial adviser suggests that his client select one of two types of bonds in which to invest \(\$ 5000\). Bond \(X\) pays a return of \(4 \%\) and has a default rate of \(2 \%\). Bond \(Y\) has a
Decide whether each experiment is a binomial experiment. If not, state the reason why.a. Selecting 20 university students and recording their class rankb. Selecting 20 students from a university and
A coin is tossed 3 times. Find the probability of getting exactly two heads.
A survey found that 2 out of 5 households own a dog. If 10 households are selected at random, find the probability that exactly two households will own a dog.
A survey from Teenage Research Unlimited (Northbrook, Illinois) found that \(30 \%\) of teenage consumers receive their spending money from part-time jobs. If 5 teenagers are selected at random, find
Solve the problem in Example 5-16 by using Table A-2.Example 5-16A coin is tossed 3 times. Find the probability of getting exactly two heads.
Public Opinion reported that 5\% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities by using the binomial table in
A report from the Secretary of Health and Human Services stated that \(70 \%\) of single vehicle traffic fatalities that occur on weekend nights involve an intoxicated driver. If a random sample of
A coin is tossed 4 times. Find the mean, variance, and standard deviation of the number of heads that will be obtained.
An 8 -sided die (with numbers 1 through 8 on the faces) is rolled 480 times. Find the mean, variance, and standard deviation of the number of \(3 \mathrm{~s}\) that will be rolled.
The Sourcebook of Criminal Justice Statistics states that \(65 \%\) of Americans favor sentencing drunk drivers to jail even if they have not caused an accident. If a random number of 1000
A random survey of Facebook users found that the probability a user visits the site on a daily basis are \(1,2,3\), or 4 times are \(0.4,0.3,0.25\), and 0.05 . If 8 customers are selected, find the
A small airport coffee shop manager found that the probabilities a customer buys 0,1 , 2 , or 3 cups of coffee are \(0.3,0.5,0.15\), and 0.05 , respectively. If 8 customers enter the shop, find the
A box contains 4 white balls, 3 red balls, and 3 blue balls. A ball is selected at random, and its color is written down. It is replaced each time. Find the probability that if 5 balls are selected,
If there are 200 typographical errors randomly distributed in a 500-page manuscript, find the probability that a given page contains exactly 3 errors.
A sales firm receives, on average, 3 calls per hour on its toll-free number. For any given hour, find the probability that it will receive the following.a. At most 3 callsb. At least 3 callsc. 5 or
If approximately \(2 \%\) of the people in a room of 200 people are left-handed, find the probability that exactly 5 people there are left-handed.
Ten people apply for a job as assistant manager of a restaurant. Five have completed college and five have not. If the manager selects 3 applicants at random, find the probability that all 3 are
A recent survey found that 3 out of 10 dog owners said that their dogs were pudgy. If 5 dog owners are randomly selected, find the probability that exactly 2 will say that their dog is pudgy.
A lot of 12 compressor tanks is checked to see whether there are any defective tanks. Three tanks are checked for leaks. If 1 or more of the 3 is defective, the lot is rejected. Find the probability
A die is rolled repeatedly. Find the probability of getting a 6 on the fourth roll.
In the United States, approximately \(42 \%\) of people have type A blood. If 4 people are selected at random, find the probability that the fourth person is the first one selected with type A blood.
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