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mathematics
statistics
Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions
Nationally, at least 60% of Ph.D. students have paid assistantships. A college dean feels that this is not true in his state, so he randomly selects 50 Ph.D. students and finds that 26 have assistantships. At α = 0.05, is the dean correct?
A report by the NCAA states that 57.6% of football injuries occur during practices. A head trainer claims that this is too high for his conference, so he randomly selects 36 injuries and finds that 17 occurred during practices. Is his claim correct, at α = 0.05?
Approximately 19.4% of the U.S. population 5 years old and older speaks a language other than English at home. In a large metropolitan area it was found that out of 400 randomly selected residents over 5 years of age, 94 spoke a language other than English at home. Is there sufficient evidence to
A coin is tossed 9 times and 3 heads appear. Can you conclude that the coin is not balanced? Use α = 0.10.
In the past, 20% of all airline passengers flew first class. In a sample of 15 passengers, 5 flew first class. At α = 0.10, can you conclude that the proportions have changed?
Show that z = - p / √pq / n can be derived from z = X - µ / σ by substituting µ = np and σ = √npq and dividing both numerator and denominator by n.
A recent survey found that 68.6% of the population own their homes. In a random sample of 150 heads of households, 92 responded that they owned their homes. At the α = 0.01 level of significance, does that suggest a difference from the national proportion?Perform each of the following steps.a.
It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance would you conclude that this was a significant difference?Perform each of the following steps.a. State
Health issues due to being overweight affect all age groups. Of children and adolescents 6–11 years of age, 18.8% are found to be overweight. A school district randomly sampled 130 in this age group and found that 20 were considered overweight. At α = 0.05 is this less than the national
The percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large university health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians at the
Of U.S. residents traveling overseas, 47% were women and 53% were men. A random sample of 500 travelers on a large airline revealed that of those 500, 263 were women. Does this differ from the national percentage at the 0.05 level of significance?Perform each of the following steps.a. State the
Using Table G, find the critical value(s) for each, show the critical and noncritical regions, and state the appropriate null and alternative hypotheses. Use σ2 = 225.a. α = 0.05, n = 18, right-tailedb. α = 0.10, n = 23, left-tailedc. α = 0.05, n = 15, two-tailedd. α = 0.10, n = 8,
A statistics professor is used to having a variance in his class grades of no more than 100. He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below.) At α = 0.05, can it be concluded that the variance in grades exceeds 100?
A researcher claims that the standard deviation of the number of deaths annually from tornadoes in the United States is less than 35. If a sample of 11 randomly selected years had a standard deviation of 32, is the claim believable? Use α = 0.05.
It has been reported that the standard deviation of the speeds of drivers on Interstate 75 near Findlay, Ohio, is 8 miles per hour for all vehicles. A driver feels from experience that this is very low. A survey is conducted, and for 50 drivers the standard deviation is 10.5 miles per hour. At α =
Room and board fees for a random sample of independent religious colleges are listed below.Estimate the standard deviation in costs based on s R / 4. Is there sufficient evidence to conclude that the sample standard deviation differs from this estimated amount? Use α =
A sample of heights (in feet) of active volcanoes in North America, outside of Alaska, is listed below. Is there sufficient evidence that the standard deviation in heights of volcanoes outside Alaska is less than the standard deviation in heights of Alaskan volcanoes, which is 2385.9 feet? Use
A manufacturing process produces machine parts with measurements the standard deviation of which must be no more than 0.52 mm. A random sample of 20 parts in a given lot revealed a standard deviation in measurement of 0.568 mm. Is there sufficient evidence at α = 0.05 to conclude that the standard
Using Table G, find the P-value interval for each x2 test value. a. x2 = 29.321, n = 16, right-tailed b. x2 = 10.215, n = 25, left-tailed c. x2 = 24.672, n = 11, two-tailed d. x2 = 23.722, n = 9, right-tailed e. x2 = 13.974, n = 28, two-tailed f. x2 = 10.571, n = 19, left-tailed g. x2 = 12.144, n =
A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60. A sample of major brands of syrup is selected, and the number of calories is shown. At α = 0.10, can the claim be rejected?
Daily weather observations for southwestern Pennsylvania for the first three weeks of January show daily high temperatures as follows: 55, 44, 51, 59, 62, 60, 46, 51, 37, 30, 46, 51, 53, 57, 57, 39, 28, 37, 35, and 28 degrees Fahrenheit. The normal standard deviation in high temperatures for this
Test the claim that the standard deviation of the number of aircraft stolen each year in the United States is less than 15 if a sample of 12 years had a standard deviation of 13.6. Use α = 0.05.
The number of carbohydrates found in a random sample of fast-food entrees is listed below. Is there sufficient evidence to conclude that the variance differs from 100? Use the 0.05 level of significance.
The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.2 minutes or less. A sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is
A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.03 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At α = 0.05, can we reject the
Potassium is important to good health in keeping fluids and minerals balanced and blood pressure low. High-potassium foods are those that contain more than 200 mg per serving. The amounts of potassium for a random sample are shown. At α = 0.10 is the standard deviation of the
The average weekly earnings in the leisure and hospitality industry group for a recent year was $273. A random sample of 40 workers showed weekly average earnings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs
The average one-way airfare from Pittsburgh to Washington, D.C., is $236. A random sample of 20 one-way fares during a particular month had a mean of $210 with a standard deviation of $43. At α = 0.02, is there sufficient evidence to conclude a difference from the stated mean? Use the sample
The IRS examined approximately 1% of individual tax returns for a specific year, and the average recommended additional tax per return was $19,150. Based on a random sample of 50 returns, the mean additional tax was $17,020. If the population standard deviation is $4080, is there sufficient
The average time it takes a person in a one-person canoe to complete a certain river course is 47 minutes. Because of rapid currents in the spring, a group of 10 people traverse the course in an average of 42 minutes. The standard deviation, known from previous trips, is 7 minutes. Test the claim
Workers with a formal arrangement with their employer to be paid for time worked at home worked an average of 19 hours per week. A random sample of 15 mortgage brokers indicated that they worked a mean of 21.3 hours per week with a standard deviation of 6.5 hours. At α = 0.05, is there sufficient
A survey taken several years ago found that the average time a person spent reading the local daily newspaper was 10.8 minutes. The standard deviation of the population was 3 minutes. To see whether the average time had changed since the newspaper’s format was revised, the newspaper editor
A meteorologist claims that the average of the highest temperatures in the United States is 98º. A random sample of 50 cities is selected, and the highest temperatures are recorded. The data are shown. At α = 0.05, can the claim be rejected? Assume σ = 7.71.Perform each of the following
Nationally 60.2% of federal prisoners are serving time for drug offenses. A warden feels that in his prison the percentage is even higher. He surveys 400 inmates’ records and finds that 260 of the inmates are drug offenders. At α = 0.05, is he correct?Perform each of the following steps.a. State
It has been reported that 59.3% of U.S. school lunches served are free or at a reduced price. A random sample of 300 children in a large metropolitan area indicated that 156 of them received lunch free or at a reduced price. At the 0.01 level of significance, is there sufficient evidence to
An MP3 manufacturer claims that 65% of teenagers 13 to 16 years old have their own MP3 player. A researcher wishes to test the claim and selects a random sample of 80 teenagers. She finds that 57 have their own MP3 players. At α = 0.05, should the claim be rejected? Use the P-value method.Perform
The use of both alcohol and tobacco by high school seniors has declined in the last 30 years. Alcohol use is down from 68.2 to 43.1%, and the use of cigarettes by high school seniors has decreased from 36.7 to 20.4%. A random sample of 300 high school seniors from a large region indicated that 18%
A film editor feels that the standard deviation for the number of minutes in a video is 3.4 minutes. A sample of 24 videos has a standard deviation of 4.2 minutes. At α = 0.05, is the sample standard deviation different from what the editor hypothesized?Perform each of the following steps.a. State
The standard deviation of the fuel consumption of a certain automobile is hypothesized to be greater than or equal to 4.3 miles per gallon. A sample of 20 automobiles produced a standard deviation of 2.6 miles per gallon. Is the standard deviation really less than previously thought? Use α = 0.05
The average movie admission price for a recent year was $7.18. The population variance was 3.81. A random sample of 15 theater admission prices had a mean of $8.02 with a standard deviation of 2.08. At α = 0.05 is there sufficient evidence to conclude a difference from the population
A random sample of the number of games played by individual NBA scoring leaders is found below. Is there sufficient evidence to conclude that the variance in games played differs from 40? Use α = 0.05.Perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the
To see whether people are keeping their car tires inflated to the correct level of 35 pounds per square inch (psi), a tire company manager selects a sample of 36 tires and checks the pressure. The mean of the sample is 33.5 psi, and the population standard deviation is 3 psi. Are the tires properly
A biologist knows that the average length of a leaf of a certain full-grown plant is 4 inches. The standard deviation of the population is 0.6 inch. A sample of 20 leaves of that type of plant given a new type of plant food had an average length of 4.2 inches. Is there reason to believe that the
Based on information from the U.S. Census Bureau, the mean travel time to work in minutes for all workers 16 years old and older was 25.3 minutes. A large company with offices in several states randomly sampled 100 of its workers to ascertain their commuting times. The sample mean was 23.9 minutes,
A random sample of the average debt (in dollars) at graduation from 30 of the top 100 public colleges and universities is listed below. Is there sufficient evidence at α = 0.01 to conclude that the population mean debt at graduation is less than $18,000? Assume σ = 2605.Perform each of the
An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the claim, 35 individuals were given the product; the average time until relief was 9.25 minutes. From past studies, the standard deviation of the population is known to be 2
The average monthly rent for a one-bedroom home in San Francisco is $1229. A random sample of 15 one-bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standard deviation is $250. At α = 0.05, can we conclude that the monthly rent outside San Francisco
Nationwide, the average salary of actuaries who achieve the rank of Fellow is $150,000. An insurance executive wants to see how this compares with Fellows within his company. He checks the salaries of eight Fellows and finds the average salary to be $155,500 with a standard deviation of $15,000.
Is lighter better? A random sample of men€™s soccer shoes from an international catalog had the following weights (in ounces).At α = 0.05 can it be concluded that the average weight is less than 10 ounces?Perform each of the following steps.a. State the hypotheses and identify the claim.b.
Once down to about 15, the world€™s only wild flock of whooping cranes now numbers a record 237 birds in its Texas Coastal Bend wintering ground (www.SunHerald.com). The average whooping crane egg weighs 208 grams. A new batch of eggs was recently weighed, and their weights are listed below. At
Nationwide 13.7% of employed wage and salary workers are union members (down from 20.1% in 1983). A random sample of 300 local wage and salary workers showed that 50 belonged to a union. At α = 0.05, is there sufficient evidence to conclude that the proportion of union membership differs from
A real estate agent compares the selling prices of homes in two municipalities in southwestern Pennsylvania to see if there is a difference. The results of the study are shown. Is there enough evidence to reject the claim that the average cost of a home in both locations is the same? Use α =
In a study of women science majors, the following data were obtained on two groups, those who left their profession within a few months after graduation (leavers) and those who remained in their profession after they graduated (stayers). Test the claim that those who stayed had a higher science
A survey of 1000 students nationwide showed a mean ACT score of 21.4. A survey of 500 Ohio scores showed a mean of 20.8. If the population standard deviation in each case is 3, can we conclude that Ohio is below the national average? Use a = 0.05.a. State the hypotheses and identify the claim.b.
The average per capita income for Wisconsin is reported to be $37,314, and for South Dakota it is $37,375€”almost the same thing. A random sample of 50 workers from each state indicated the following sample statistics.At α = 0.05 can we conclude a difference in means of the personal
The average monthly Social Security benefit in 2004 for retired workers was $954.90 and for disabled workers was $894.10. Researchers used data from the Social Security records to test the claim that the difference in monthly benefits between the two groups was greater than $30. Based on the
In the study cited in Exercise 11, the researchers collected the data shown here on a self esteem questionnaire. At α = 0.05, can it be concluded that there is a difference in the self-esteem scores of the two groups? Use the P-value method.a. State the hypotheses and identify the claim.b. Find
The dean of students wants to see whether there is a significant difference in ages of resident students and commuting students. She selects a sample of 50 students from each group. The ages are shown here. At α = 0.05, decide if there is enough evidence to reject the claim of no difference in
Two groups of students are given a problem-solving test, and the results are compared. Find the 90% confidence interval of the true difference in means.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the
The average credit card debt for a recent year was $9205. Five years earlier the average credit card debt was $6618. Assume sample sizes of 35 were used and the population standard deviations of both samples were $1928. Is there enough evidence to believe that the average credit card debt has
Adults aged 16 or older were assessed in three types of literacy in 2003: prose, document, and quantitative. The scores in document literacy were the same for 19- to 24-year-olds and for 40- to 49-year-olds. A random sample of scores from a later year showed the following statistics.Construct a 95%
When a researcher selects all possible pairs of samples from a population in order to find the difference between the means of each pair, what will be the shape of the distribution of the differences when the original distributions are normally distributed? What will be the mean of the
Two brands of batteries are tested, and their voltage is compared. The data follow. Find the 95% confidence interval of the true difference in the means. Assume that both variables are normally distributed.
A researcher claims that students in a private school have exam scores that are at most 8 points higher than those of students in public schools. Random samples of 60 students from each type of school are selected and given an exam. The results are shown. At a 0.05, test the claim.
The average sales price of new one-family houses in the Midwest is $250,000 and in the South is $253,400. A random sample of 40 houses in each region was examined with the following results. At the 0.05 level of significance can it be concluded that the difference in mean sales price for the two
The average earnings of year-round full-time workers with bachelor’s degrees or more is $88,641 for men and $58,000 for women—a difference of slightly over $30,000 a year. One hundred of each were sampled, resulting in a sample mean of $90,200 for men, and the population standard deviation is
What two assumptions must be met when you are using the z test to test differences between two means? Can the sample standard deviations s1 and s2 be used in place of the population standard deviations 1 and s2?
A researcher wishes to see if the average length of the major rivers in the United States is the same as the average length of the major rivers in Europe. The data (in miles) of a sample of rivers are shown. At a = 0.01, is there enough evidence to reject the claim? Assume σ1= 450 and σ2 =
California and New York lead the list of average teachers€™ salaries. The California yearly average is $64,421 while teachers in New York make an average annual salary of $62,332. Random samples of 45 teachers from each state yielded the following.At a = 0.10 is there a difference in means of
The Bureau of the Census reports that the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida, is approximately 29 minutes. To see if their commuting times appear to be any different in the winter, random samples of 40 drivers were surveyed in each city and the
At age 9 the average weight (21.3 kg) and the average height (124.5 cm) for both boys and girls are exactly the same. A random sample of 9-year-olds yielded these results. Estimate the mean difference in height between boys and girls with 95% confidence. Does your interval support the given
The average length of €œshort hospital stays€ for men is slightly longer than that for women, 5.2 days versus 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At α = 0.01, is there sufficient evidence to conclude that the average hospital
The mean for the number of weeks 15 New York Times hard-cover fiction books spent on the bestseller list is 22 weeks. The standard deviation is 6.17 weeks. The mean for the number of weeks 15 New York Times hard-cover nonfiction books spent on the list is 28 weeks. The standard deviation is 13.2
Find the 95% confidence interval for the difference of the means in Exercise 8 of this section.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.
Nielsen Media Research, children (ages 2€“11) spend an average of 21 hours 30 minutes watching television per week while teens (ages 12€“17) spend an average of 20 hours 40 minutes. Based on the sample statistics obtained below, is there sufficient evidence to conclude a difference in
An agent claims that there is no difference between the pay of safeties and linebackers in the NFL. A survey of 15 safeties found an average salary of $501,580, and a survey of 15 linebackers found an average salary of $513,360. If the standard deviation in the first sample is $20,000 and the
The data show the number of students attending cyber charter schools in Allegheny County and the number of students attending cyber schools in counties surrounding Allegheny County. At α = 0.01 is there enough evidence to support the claim that the average number of students in school districts
Whiting, Indiana, leads the €œTop 100 Cities with the Oldest Houses€ list with the average age of houses being 66.4 years. Farther down the list resides Franklin, Pennsylvania, with an average house age of 59.4 years. Researchers selected a random sample of 20 houses in each city and
Health Care Knowledge Systems reported that an insured woman spends on average 2.3 days in the hospital for a routine childbirth, while an uninsured woman spends on average 1.9 days. Assume two samples of 16 women each were used in both samples. The standard deviation of the first sample is equal
The number of points held by a sample of the NHL€™s highest scorers for both the EasternConference and the Western Conference is shown below. At α = 0.05, can it be concluded that there is a difference in means based on these data?a. State the hypotheses and identify the claim.b. Find the
A random sample of enrollments from medical schools that specialize in research and from those that are noted for primary care is listed. Find the 90% confidence interval for the difference in the means.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test
The out-of-state tuitions (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Find the 95% confidence interval for the difference in the means.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the
A tax collector wishes to see if the mean values of the tax-exempt properties are different for two cities. The values of the tax-exempt properties for the two samples are shown. The data are given in millions of dollars. A a 0.05, is there enough evidence to support the tax collector€™s claim
The mean noise level of 20 areas designated as “casualty doors” was 63.1 dBA, and the standard deviation is 4.1 dBA. The mean noise level for 24 areas designated as operating theaters was 56.3 dBA, and the standard deviation was 7.5 dBA. At α = 0.05, can it be concluded that there is a
The mean age of a sample of 25 people who were playing the slot machines is 48.7 years, and the standard deviation is 6.8 years. The mean age of a sample of 35 people who were playing roulette is 55.3 with a standard deviation of 3.2 years. Can it be concluded at α = 0.05 that the mean age of
The number of grams of carbohydrates contained in 1-ounce servings of randomly selected chocolate and nonchocolate candy is listed here. Is there sufficient evidence to conclude that the difference in the means is significant? Use α = 0.10.a. State the hypotheses and identify the claim.b. Find
A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a sample of 26 elementary school teachers is $48,256, and the sample standard deviation is
The weights in ounces of a sample of running shoes for men and women are shown.Test the claim that the means are different. Use the P-value method with α = 0.05.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e.
Upright vacuum cleaners have either a hard body type or a soft body type. Shown are the weights in pounds of a sample of each type. At a 0.05, can it be concluded that the means of the weights are different?a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the
Find the 95% confidence interval for the difference of the means in Exercise 3 of this section.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.
A random sample of six music students played a short song, and the number of mistakes each student made was recorded. After they practiced the song 5 times, the number of mistakes each student made was recorded. The data are shown. At α = 0.05, can it be concluded that there was a decrease in
Instead of finding the mean of the differences between X1 and X2 by subtracting X1 = X2, you can find it by finding the means of X1 and X2 and then subtracting the means. Show that these two procedures will yield the same results.a. State the hypotheses and identify the claim.b. Find the critical
A sample of non-English majors at a selected college was used in a study to see if the student retained more from reading a 19th-century novel or by watching it in DVD form. Each student was assigned one novel to read and a different one to watch, and then they were given a 20-point written quiz on
As an aid for improving students’ study habits, nine students were randomly selected to attend a seminar on the importance of education in life. The table shows the number of hours each student studied per week before and after the seminar. At α = 0.10, did attending the seminar increase the
An obstacle course was set up on a campus, and 10 volunteers were given a chance to complete it while they were being timed. They then sampled a new energy drink and were given the opportunity to run the course again. The €œbefore€ and €œafter€ times in seconds are shown below. Is
Students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. At α = 0.05, is there sufficient evidence that there is a difference in the mean number of hours slept?a. State the hypotheses and identify the claim.b. Find the critical value(s).c.
At a recent PGA tournament (the Honda Classic at Palm Beach Gardens, Florida) the following scores were posted for eight randomly selected golfers for two consecutive days. At α = 0.05, is there evidence of a difference in mean scores for the two days?a. State the hypotheses and identify the
A composition teacher wishes to see whether a new grammar program will reduce the number of grammatical errors her students make when writing a two-page essay. The data are shown here. At α = 0.025, can it be concluded that the number of errors has been reduced?a. State the hypotheses and
A veterinary nutritionist developed a diet for overweight dogs. The total volume of food consumed remains the same, but one half of the dog food is replaced with a low-calorie €œfiller€ such as canned green beans. Six overweight dogs were randomly selected from her practice and were put on
A researcher wanted to compare the pulse rates of identical twins to see whether there was any difference. Eight sets of twins were selected. The rates are given in the table as number of beats per minute. At a 0.01, is there a significant difference in the average pulse rates of twins? Find the
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