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mathematics
statistics
Statistical Reasoning For Everyday Life 4th Edition Jeff Bennett, Bill Briggs, Mario F. Triola - Solutions
A study by Stanford University researchers for the Office of National Drug Control Policy and the Department of Health and Human Services concluded that 98% of the top rental films involve drugs, drinking, or smoking. Assume that this study is based on the top 400 rental films.a. Use the results of
A study commissioned by the U.S. Department of Education concluded that 44% of teenagers cite grades as their greatest source of pressure. The study was based on responses from 1,015 teenagers. What is the 95% confidence interval?
Prior to a statewide election for the U.S. Senate, three polls are conducted. In the first poll, 780 of 1,500 voters favor candidate Martinez. In the second poll, 1,285 of 2,500 voters favor Martinez. In the third poll, 1,802 of 3,500 voters favor Martinez. Find the 95% confidence intervals for all
The Bureau of Labor Statistics estimates the unemployment rate in the United States monthly by surveying 60,000 individuals.a. In one month, 3.4% of the 60,000 individuals surveyed are found to be unemployed. Find the margin of error for this estimate. Is the precision (nearest tenth of a percent)
A poll finds that 54% of the population approves of the job that the President is doing; the poll has a margin of error of 4% (assuming a 95% degree of confidence).a. What is the 95% confidence interval for the true population percentage that approves of the President's performance?b. What was the
Two-thirds (or 66.6%) of 626 Colorado residents polled by Talmey-Drake Research & Strategy Inc. said they backed a bill pending in the legislature that would standardize laws on granting concealed-weapon permits to gun owners. The bill would force local law enforcement to grant such permits to
In a Pew Research Center poll, 73% of 3011 adults surveyed said that they use the Internet. A reporter claims that the results are not very good because they are based on a survey of only 0.001% of the adults in the United States, and that percentage is too small to be meaningful. Is that claim
The 95% confidence interval given in Example 1 is based on a sample size of 150. If the sample size is increased, the confidence interval will become smaller (or narrower). Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
A reporter for the Kingston Chronicle claims that any good confidence interval should be based on a sample that is at least 5% of the population size. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Sample size = 1,000, sample proportion = 0.4Assume that population proportions are to be estimated from the samples described. In each case, find the approximate margin of error and 95% confidence interval.
A study is designed to determine the proportion of men who weigh more than 195 pounds, so the null hypothesis is p. = 195 pounds and the alternative hypothesis is p. > 195 pounds. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain
In interpreting a P-value of 0.45, a researcher states that the results are statistically significant because the P-value is less than 0.5, indicating that the results are not likely to occur by chance. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is
In testing a method of gender selection, 40 couples are given a treatment designed to increase the likelihood of a girl, and each couple has one baby. a. If the 40 babies include exactly 22 girls, would you consider this result statistically significant or would you attribute it to random
In testing a method of gender selection, 200 couples are given a treatment designed to increase the likelihood of a girl, and each couple has one baby. a. If the 200 babies include exactly 130 girls, would you consider this result statistically significant or would you attribute it to random
Exercises 15, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. Package labeling indicates that Twix candy bars have an amount of caloric content equal to 250 calories.
Exercises 16, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. A high school principal claims that the mean SAT score of seniors at his school is less than the national average of 1518.
Exercises 17, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. The Chief Operations Officer of a medical facility claims that treatments can increase the probability that a baby will be a girl so that the
Exercises 18, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. The quality control manager at a manufacturing company claims that the proportion of defective carbon monoxide detectors is less than 0.04.
Exercises 19, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim.A sales representative claims that her vending machines dispense coffee so that the mean amount supplied is equal to 10 ounces.
What is a null hypothesis? What notation is used for a null hypothesis? What is an alternative hypothesis? What notation is used for an alternative hypothesis?
Exercises 20, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. The Food and Drug Administration claims that a pharmaceutical company is producing aspirin tablets with a mean amount of aspirin that is less
Exercises 21, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim. A high school teacher claims that the majority of her students do not know what the term Holocaust refers to.
Exercises 22, formulate the null and alternative hypotheses for a hypothesis test. State clearly the two possible conclusions that address the given claim.An educator claims that less than 20% of college graduates smoke.
A random sample of 100 births has 48 male babies. Is this result significant at the 0.05 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A random sample of 100 births has 45 male babies. Is this result significant at the 0.01 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A random sample of 100 births has 40 male babies. Is this result significant at the 0.01 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A random sample of 100 births has 40 male babies. Is this result significant at the 0.05 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A random sample of 100 births has 35 male babies. Is this result significant at the 0.01 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A random sample of 100 births has 32 male babies. Is this result significant at the 0.01 level? What is the P-value for this result?Assume that male births and female births are equally likely. The following table shows the probabilities of various numbers of male babies in a random sample of 100
A researcher wants to test the claim that the mean weight of male airline passengers, including carry-on baggage, is 195 lb. Identify the three different possible expressions that could be used for the alternative hypothesis.
To test the claim that a particular drug lowers blood pressure, sample data are collected and a hypothesis test is used, and we form this conclusion: "The study proves that the drag lowers blood pressure in everyone." Decide whether the statement makes sense (or is clearly true) or does not make
A researcher is convinced that she can show that a new drag is effective in lowering LDL cholesterol. She claims that the P-value of 0.20 supports her claim of a lower mean level of LDL cholesterol. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly
In testing a claim that the mean LDL cholesterol level is less than 130 mg/dL the researcher states the alternative hypothesis as µ < 130 mg/dL. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
After conducting a hypothesis test, a researcher concludes that there is sufficient sample evidence to support the null hypothesis that ix = 75. Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.
Briefly describe what each of the variables n, x, s. a. and u. represent in hypothesis tests of a claim made about a population mean.
When a consumer group is testing the claim that the mean amount of aspirin in tablets is 350 milligrams, it is extremely important not to reject a true null hypothesis wrongly. Thus, it is better to choose 0.01 than 0.05 for the significance level. Does this statement make sense or not? Explain
Because the significance level is the probability of making a type I error, it is wise to select a significance level of zero so that there is no probability of making that error. Does this statement make sense or not? Explain clearly.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: u. < 75, n = 100, x = 70, a = 15.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: x < 75, n = 36, x = 72, a = 15.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: x > 12, n = 64, x = 14, a = 2.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: µ > 1007, n = 225, x= 1021, a = 35.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: µ ≠ 2.55, n = 100, x = 2.58, a = 0.29.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: µ ≠ 156.2, n = 225, x = 155.5, a = 29.
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: µ ≠ 0.88, n = 50, x = 0.75, a = 0.18.
A student in a statistics class conducts a project designed to test the claim that wait times at McDonald's drive-up windows have a mean that is less than 5 minutes. She collects sample data from wait times at five randomly selected McDonald's locations that are within 30 miles of her home. What is
Find the value of the standard score, z, and determine whether the alternative hypothesis is supported at a 0.05 significance level.Ha: µ ≠ 877, n = 90,3c = 921, a = 52.
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.-0.4 for Ha: u < 25Formulate the null and alternative hypothesis for a hypothesis test. State clearly the two possible
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.-2.4 for Ha: u < 121Formulate the null and alternative hypothesis for a hypothesis test. State clearly the two possible
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.1.9 for Ha: u < 36.35Assume that male births and female births are equally likely. The following table shows the probabilities
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.1.5 for Ha: u Assume that male births and female births are equally likely. The following table shows the probabilities of various
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 1.6 for Ha: u < 0.389
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = –2.0 for Ha: u < 172
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 1.7 for Ha: u < 75
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 1.9 for Ha: u < 25.7
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 2.7 for Ha: u < 19.4
What is a type I error? What is a type II error?
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 3.5 for Ha: u < 75
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = –2.7 for Ha: u < 1007
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = –1.1 for Ha: u < 149.6
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 0.15 for Ha: u < 90.3
Use Table 5.1 to find the P-value that corresponds to the standard z-score, and determine whether the alternative hypothesis is supported at the 0.05 significance level.z = 3.5 for Ha: u < 1022
Assume that you are testing an alternative hypothesis of the form Ha: µ > claimed value. If the sample mean has a standard score of z = —1.0, what do you conclude? Why is it not necessary to actually conduct the formal hypothesis test?
Assume that you are testing an alternative hypothesis of the form Ha: u, < claimed value. If the sample mean has a standard score of z = 8.5, what do you conclude? Why is it not necessary to actually conduct the formal hypothesis test?
A Roper poll used a sample of 100 randomly selected car owners. Within the sample, the mean time of ownership for a single car was 7.01 years with a standard deviation of 3.74 years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than 7.5
According to a study by the Centers for Disease Control, the national mean hospital stay after childbirth is 2.0 days. Reviewing records at her own hospital, a hospital administrator calculates that the mean hospital stay for a sample of 81 women after childbirth is 2.2 days with a standard
A random sample of 36 cans of regular Coke is obtained and the contents are measured. The sample mean is 12.19 oz and the standard deviation is 0.11 oz. Test the claim that the contents of all such cans have a mean different from 12.00 oz, as indicated by the label.
Consider a test of the claim that with a new device installed, the mean fuel consumption of cars is reduced by 0.08 miles per gallon. The resulting P-value is 0.009. Is the mean fuel consumption reduction statistically significant? Does the mean fuel consumption reduction of 0.08 miles per gallon
The manufacturers of motorcycles must produce axles that meet specified dimensions. In particular, the diameters of the axles must be 8.50 centimeters. The axles in a sample of n = 64 axles have a mean diameter of 8.56 centimeters with a standard deviation of 0.24 centimeter. Test the claim that
The cold medicine Dozenol lists 600 milligrams of acetominophen per fluid ounce as an active ingredient. The Food and Drug Administration tests 65 one-ounce samples of the medicine and finds that the mean amount of acetominophen for the sample is 589 milligrams with a standard deviation of 21
A simple random sample of 50 adults is obtained, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.23. The population standard deviation for red blood cell counts is 0.54. Test the claim that the sample is from a population with a mean less than 5.4,
According to the Energy Information Administration (Federal Highway Administration data), the average gas mileage of all automobiles is 21.4 miles per gallon. For a random sample of 40 sport utility vehicles (SUVs), the mean gas mileage is 19.8 miles per gallon with a standard deviation of 3.5
A random sample of 40 new baseballs is obtained. Each ball is dropped onto a concrete surface, and the bounce heights have a mean of 92.67 inches and a standard deviation of 1.79 inches (based on data from USA Today). Test the claim that the new baseballs have a mean bounce height that is less than
Researchers developed a questionnaire to identify compulsive buyers. A random sample of 32 subjects who identified themselves as compulsive buyers was obtained, and they had a mean questionnaire score of 0.83 with a standard deviation of 0.24 (based on data from "A Clinical Screener for Compulsive
According to the U.S. Department of the Treasury, the mean weight of a quarter is 5.670 grams. A random sample of 50 quarters has a mean weight of 5.622 grams with a standard deviation of 0.068 gram. Test the claim that the mean weight of quarters in circulation is 5.670 grams.
The mean birth weight of male babies born to 121 mothers taking a vitamin supplement is 3.67 kilograms with a standard deviation of 0.66 kilogram (based on data from the New York State Department of Health). Test the claim that the mean birth weight of all babies born to mothers taking the vitamin
The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming that a is known to be 121.8 lb, test the claim that the population mean of all such bear weights is
When 70 convicted embezzlers were randomly selected, the mean length of prison terms was found to be 22.1 months and the standard deviation was 8.6 months (based on data from the U.S. Department of Justice). Jane Fleming is running for political office on a platform of tougher treatment of
In hypothesis tests, the P-value is always the same as the significance level.Does this statement make sense or not? Explain clearly.
A simple random sample of 40 salaries of NCAA football coaches in the NCAA has a mean of $415,953. The standard deviation of all salaries of NCAA football coaches is $463,364. Test the claim that the mean salary of a football coach in the NCAA is less than $500,000.
A null and alternative hypothesis are given. Without using the terms "null hypothesis" and "alternative hypothesis," identify the type I error and identify the type II error. H0. The patient is free of a particular disease. Ha: The patient has the disease.
A null and alternative hypothesis are given. Without using the terms "null hypothesis" and "alternative hypothesis," identify the type I error and identify the type II error. H0. The defendant is not guilty Ha: The defendant is guilty.
A null and alternative hypothesis are given. Without using the terms "null hypothesis" and "alternative hypothesis," identify the type I error and identify the type II error. H0. The lottery is fair. Ha: The lottery is biased.
A null and alternative hypothesis are given. Without using the terms "null hypothesis" and "alternative hypothesis," identify the type I error and identify the type II error. H0. The mean length of a bolt in the suspension system of new Audi cars is 3.456 centimeters. Ha: The mean length of a bolt
In a hypothesis test, a P-value of 0.001 indicates that you should support the alternative hypothesis. Does this statement make sense or not? Explain clearly.
What do p, p, and P-value represent?
A survey showed that among 785 randomly selected subjects who completed four years of college, 144 smoke and the others do not smoke (based on data from the American Medical Association). Test the claim that the rate of smoking among those with four years of college is less than the 27% rate for
A study commissioned by the U.S. Department of Education, based on responses from 1,015 randomly selected teenagers, concluded that 44% of teenagers cite grades as their greatest source of pressure. Test the claim that fewer than half of all teen-agers in the population feel that grades are their
In a recent year, 125.8 million adults, or 58.6% of the adult American population, were married. In a New England town, a simple random sample of 1,445 adults includes 56.0% who are married. Test the claim that this sample comes from a population with a married percentage of less than 58.6%.
A Department of Health and Human Services study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997) to 9.9% now. Suppose a survey in a large high school reveals that, in a random sample of 1,050 students, 98 report using illegal drugs. Test the principal's
According to recent estimates, 12.1% of the 4,342 people in Custer County, Idaho, live in poverty. Assume that the people in this county represent a random sample of all people in Idaho. Based on this sample, test the claim that the poverty rate in Idaho is less than the national rate of 13.3%.
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
When 3011 adults were surveyed in a Pew Research Center poll, 2198 said that they use the Internet. Is it OK for a newspaper reporter to write that "3/4 of all adults use the Internet"? Why or why not?
According to the Energy Information Administration, 53.0% of households nationwide used natural gas for heating in 1997. A recent survey of 3,600 randomly selected households showed that 54.0% used natural gas. Use a 0.05 significance level to test the claim that the 53.0% national rate has changed.
In clinical tests of the drug Lipitor, 863 patients were treated with the drug and 19 of them experienced flu symptoms (based on data from Parke-Davis). Test the claim that the percentage of treated patients with flu symptoms is greater than the 1.9% rate for patients not given treatments.
Randomly selected cans of Coke are measured for the amount of cola, in ounces. The sample values listed below have a mean of 12.19 ounces and a standard deviation of 0.11 ounce. Assume that we want to use a 0.05 significance level to test the claim that cans of Coke have a mean amount of cola
In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from "High Dose Nicotine Patch Therapy," by Dale et al., Journal of the American Medical Association, Vol.
In a survey of 703 randomly selected workers, 429 got their jobs through networking (based on data from Taylor Nelson Sofres Research).a. Use the sample data with a 0.05 significance level to test the claim that most (more than 50% of) workers get their jobs through networking.b. If given a claim
A medical student wants to test the claim that males who smoke have pulse rates with a mean greater than 70. She collects sample data by surveying her fellow medical students. What is the fundamental flaw in his procedure?
A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. The survey is an H/e/MSNBC.COM survey in which Internet users chose whether to respond. Is it valid to use the sample results for testing the claim that
A P-value of 0.00001 is obtained when sample data are used to test the claim that the majority of car crashes occur within 5 miles of home. What does this P-value tell us?
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