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mathematics
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Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions
A U.S. Travel Data Center survey conducted for Better Homes and Gardens of 1500 adults found that 39% said that they would take more vacations this year than last year. Find the 95% confidence interval for the true proportion of adults who said that they will travel more this year.
Thirty-five percent of adult Americans are regular voters. A random sample of 250 adults in a medium-size college town were surveyed, and it was found that 110 were regular voters. Estimate the true proportion of regular voters with 90% confidence and comment on your results.
The proportion of students in private schools is around 11%.Arandom sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of students attending private schools with 95% confidence. How does your estimate compare to 11%?
A random sample of 205 college students were asked if they believed that places could be haunted, and 65 responded yes. Estimate the true proportion of college students who believe in the possibility of haunted places with 99% confidence. According to Time magazine, 37% of Americans believe that
A survey found that out of 200 workers, 168 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted three or more times an hour.
ACBS News/New York Times poll found that 329 out of 763 adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 92% confidence.
The national average for the percentage of high school graduates taking the SAT is 49%, but the state averages vary from a low of 4% to a high of 92%. A random sample of 300 graduating high school seniors was polled across a particular tristate area, and it was found that 195 had taken the SAT.
What are the properties of the t distribution?
The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Estimate the true population mean size of a university dance company with 99% confidence.21 25 32
A recent study of 28 employees of XYZ company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2 miles. Find the 95% confidence interval of the true mean. If a manager wanted to be sure that most of his employees would not be
A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the mean. If a meteorologist wanted to use the highest
The national average for the number of students per teacher for all U.S. public schools is 15.9.Arandom sample of 12 school districts from a moderately populated area showed that the mean number of students per teacher was 19.2 with a variance of 4.41. Estimate the true mean number of students per
A recent survey of 8 social networking sites has a mean of 13.1 million visitors for a specific month. The standard deviation was 4.1 million. Find the 95% confidence interval of the true mean.
A sample of 14 commuters in Chicago showed the average of the commuting times was 33.2 minutes. If the standard deviation was 8.3 minutes, find the 95% confidence interval of the true mean.
For a sample of 24 operating rooms taken in the hospital study mentioned in Exercise 19 in Section 7–1, the mean noise level was 41.6 decibels, and the standard deviation was 7.5. Find the 95% confidence interval of the true mean of the noise levels in the operating rooms.
The approximate costs for a 30-second spot for various cable networks in a random selection of cities are shown below. Estimate the true population mean cost for a 30- second advertisement on cable network with 90% confidence.14 55 165
For a group of 22 college football players, the mean heart rate after a morning workout session was 86 beats per minute, and the standard deviation was 5. Find the 90% confidence interval of the true mean for all college football players after a workout session. If a coach did not want to work his
The number of unhealthy days based on the AQI (Air Quality Index) for a random sample of metropolitan areas is shown. Construct a 98% confidence interval based on the data.61 12 6 40
A one-sided confidence interval can be found for a mean by usingWhere ta is the value found under the row labeled One tail. Find two one-sided 95% confidence intervals of the population mean for the data shown, and interpret the answers. The data represent the daily revenues in dollars from 20
Find the values for each.a. t a / 2 and n = 18 for the 99% confidence interval for the mean b. t a / 2 and n = 23 for the 95% confidence interval for the mean c. t a / 2 and n = 15 for the 98% confidence interval for the mean d. t a / 2 and n = 10 for the 90% confidence interval for
A sample of 10 networking sites for a specific month has a mean of 26.1 and a standard deviation of 4.2. Find the 99% confidence interval of the true mean.Assume that all variables are approximately normally distributed.
The prices (in dollars) for a particular model of digital camera with 6.0 megapixels and an optical 3X zoom lens are shown below for 10 online retailers. Estimate the true mean price for this particular model with 95% confidence.225 240 215
A state representative wishes to estimate the mean number of women representatives per state legislature. A random sample of 17 states is selected, and the number of women representatives is shown. Based on the sample, what is the point estimate of the mean? Find the 90% confidence interval of the
A random sample of state gasoline taxes (in cents) is shown here for 12 states. Use the data to estimate the true population mean gasoline tax with 90% confidence. Does your interval contain the national average of 44.7 cents?38. 4 40. 9 67
A sample of six recent years had an average of 573.8 workplace homicides per year with a standard deviation of 46.8. Find the 99% confidence interval of the true mean of all workplace homicides per year. If in a certain year there were 625 homicides, would this be considered unusually high?
Eight chemical elements do not have isotopes (different forms of the same element having the same atomic number but different atomic weights). A random sample of 30 of the elements that do have isotopes showed a mean number of 19.63 isotopes per element and the population a standard deviation of
A local county has a very active adult education venue. A random sample of the population showed that 189 out of 400 persons 16 years old or older participated in some type of formal adult education activities, such as basic skills training, apprenticeships, personal interest courses, and part-time
A federal report stated that 88% of children under age 18 were covered by health insurance in 2000. How large a sample is needed to estimate the true proportion of covered children with 90% confidence with a confidence interval 0.05 wide?
A study found that 73% of prekindergarten children ages 3 to 5 whose mothers had a bachelor’s degree or higher were enrolled in center-based early childhood care and education programs. How large a sample is needed to estimate the true proportion within 3 percentage points with 95% confidence?
The standard deviation of the diameter of 18 baseballs was 0.29 cm. Find the 95% confidence interval of the true standard deviation of the diameters of the baseballs. Do you think the manufacturing process should be checked for inconsistency?
A random sample of 22 lawn mowers was selected, and the motors were tested to see how many miles per gallon of gasoline each one obtained. The variance of the measurements was 2.6. Find the 95% confidence interval of the true variance
A random sample of 15 snowmobiles was selected, and the lifetime (in months) of the batteries was measured. The variance of the sample was 8.6. Find the 90% confidence interval of the true variance.
Use the data from Exercise 5 to estimate the population variance (standard deviation) in length of children’s animated films with 99% confidence.
A U.S. Travel Data Center survey reported that Americans stayed an average of 7.5 nights when they went on vacation. The sample size was 1500. Find a point estimate of the population mean. Find the 95% confidence interval of the true mean. Assume the population standard deviation was 0.8.
A researcher wishes to estimate within $25 the average cost of postage a community college spends in one year. If she wishes to be 90% confident, how large of a sample would be necessary if the population standard deviation is $80.
A random sample of 49 shoppers showed that they spend an average of $23.45 per visit at the Saturday Mornings Bookstore. The standard deviation of the population is $2.80. Find a point estimate of the population mean. Find the 90% confidence interval of the true mean.
The lengths (in minutes) of a random selection of popular children’s animated films are listed below. Estimate the true mean length of all children’s animated films with 95% confidence.93 83 76 92
For a certain urban area, in a sample of 5 months, on average 28 mail carriers were bitten by dogs each month. The standard deviation of the sample was 3. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month. Assume the variable is normally
In a survey of 1004 individuals, 442 felt that President GeorgeW. Bush spent too much time away from Washington. Find a 95% confidence interval for the true population proportion.
A U.S. Travel Data Center’s survey of 1500 adults found that 42% of respondents stated that they favor historical sites as vacations. Find the 95% confidence interval of the true proportion of all adults who favor visiting historical sites as vacations.
In a study of 200 accidents that required treatment in an emergency room, 80 occurred at work. Find the 90% confidence interval of the true proportion of accidents that occurred at work.
Define null and alternative hypotheses, and give an example of each.
List the steps in hypothesis testing.
Using the z table (Table E), find the critical value (or values) for each. a. α = 0.05, two-tailed test b. α = 0.01, left-tailed test c. α = 0.005, right-tailed test d. α = 0.01, right-tailed test e. α = 0.05, left-tailed test f. α = 0.02, left-tailed test g. α = 0.05, right-tailed test h.
For each conjecture, state the null and alternative hypotheses. a. The average age of community college students is 24.6 years. b. The average income of accountants is $51,497. c. The average age of attorneys is greater than 25.4 years. d. The average score of high school basketball games is less
What is meant by a type I error? A type II error? How are they related?
Explain the difference between a one-tailed and a two-tailed test.
What is meant by the critical region? The noncritical region?
The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.57. Can it be
A real estate agent claims that the average price of a home sold in Beaver County, Pennsylvania, is $60,000.Arandom sample of 36 homes sold in the county is selected, and the prices in dollars are shown. Is there enough evidence to reject the agent’s claim at α = 0.05? Assume σ =
The average college student goes through 500 disposable cups in a year. To raise environmental awareness, a student group at a large university volunteered to help count how many cups were used by students on their campus. A random sample of 50 students’ results found that they used a mean of 476
The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10,798. Do these results indicate that the
The mean age of Senators in the 109th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α = 0.05, is there sufficient evidence that state senators are on average younger than
State whether the null hypothesis should be rejected on the basis of the given P-value. a. P-value = 0.258, α = 0.05, one-tailed test b. P-value = 0.0684, α = 0.10, two-tailed test c. P-value = 0.0153, α = 0.01, one-tailed test d. P-value = 0.0232, α = 0.05, two-tailed test e. P-value = 0.002,
A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the population is 3.5 gallons. Find the P-value for the test. On the basis of the
A study found that the average stopping distance of a school bus traveling 50 miles per hour was 264 feet. A group of automotive engineers decided to conduct a study of its school buses and found that for 20 buses, the average stopping distance of buses traveling 50 miles per hour was 262.3 feet.
A store manager hypothesizes that the average number of pages a person copies on the store’s copy machine is less than 40. A sample of 50 customers’ orders is selected. At α = 0.01, is there enough evidence to support the claim? Use the P-value hypothesis-testing method. Assume σ = 30.9.
A health researcher read that a 200-pound male can burn an average of 546 calories per hour playing tennis. Thirty-six males were randomly selected and tested. The mean of the number of calories burned per hour was 544.8. Test the claim that the average number of calories burned is actually less
It has been reported that the average credit card debt for college seniors at the college book store for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds
A special cable has a breaking strength of 800 pounds. The standard deviation of the population is 12 pounds. A researcher selects a sample of 20 cables and finds that the average breaking strength is 793 pounds. Can he reject the claim that the breaking strength is 800 pounds? Find the P-value.
The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. At α = 0.05, can it be concluded that the average farm in Oregon differs from the national mean? Use the P-value
Ten years ago, the average acreage of farms in a certain geographic region was 65 acres. The standard deviation of the population was 7 acres. A recent study consisting of 22 farms showed that the average was 63.2 acres per farm. Test the claim, at α = 0.10, that the average has not changed by
A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is
A motorist claims that the South Boro Police issue an average of 60 speeding tickets per day. These data show the number of speeding tickets issued each day for a period of one month. Assume σ is 13.42. Is there enough evidence to reject the motorist’s claim at α = 0.05? Use the P-value method.
A manager states that in his factory, the average number of days per year missed by the employees due to illness is less than the national average of 10. The following data show the number of days missed by 40 employees last year. Is there sufficient evidence to believe the manager€™s statement
The president of a company states that the average hourly wage of her employees is $8.65. A sample of 50 employees has the distribution shown. At α = 0.05, is the president’s statement believable? Assume σ = 0.105.Class
A researcher estimates that the average revenue of the largest businesses in the United States is greater than $24 billion. A sample of 50 companies is selected, and the revenues (in billions of dollars) are shown. At α = 0.05, is there enough evidence to support the researcher’s claim? Assume
The average “moviegoer” sees 8.5 movies a year. A moviegoer is defined as a person who sees at least one movie in a theater in a 12-month period. A random sample of 40 moviegoers from a large university revealed that the average number of movies seen per person was 9.6. The population standard
According to the Digest of Educational Statistics, a certain group of preschool children under the age of one year each spends an average of 30.9 hours per week in nonparental care. A study of state university center-based programs indicated that a random sample of 32 infants spent an average of
The average production of peanuts in Virginia is 3000 pounds per acre. A new plant food has been developed and is tested on 60 individual plots of land. The mean yield with the new plant food is 3120 pounds of peanuts per acre, and the population standard deviation is 578 pounds. At α = 0.05, can
The average 1-year-old (both genders) is 29 inches tall. A random sample of 30 1-year olds in a large day care franchise resulted in the following heights. At α = 0.05, can it be concluded that the average height differs from 29 inches? Assume σ = 2.61.Perform each of the following steps.a.
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with σ = $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal
The average cost of owning and operating an automobile is $8121 per 15,000 miles including fixed and variable costs. A random survey of 40 automobile owners revealed an average cost of $8350 with a population standard deviation of $750. Is there sufficient evidence to conclude that the average is
In what ways is the t distribution similar to the standard normal distribution? In what ways is the t distribution different from the standard normal distribution?
Men spend an average of 29 minutes per day on weekends and holidays exercising and playing sports. They spend an average of 23 minutes per day reading. A random sample of 25 men resulted in a mean of 35 minutes exercising with a standard deviation of 6.9 minutes and an average of 20.5 minutes
Teens are reported to watch the fewest total hours of television per week of all the demographic groups. The average television viewing for teens on Sunday from 1:00 to 7:00 PM. is 1 hour 13 minutes. A random sample of local teens disclosed the following times for Sunday afternoon television
AU.S. Web Usage Snapshot indicated a monthly average of 36 Internet visits per user from home. A random sample of 24 Internet users yielded a sample mean of 42.1 visits with a standard deviation of 5.3. At the 0.01 level of significance can it be concluded that this differs from the national
During a recent year the average cost of making a movie was $54.8 million. This year, a random sample of 15 recent action movies had an average production cost of $62.3 million with a variance of $90.25 million. At the 0.05 level of significance, can it be concluded that it costs more than average
The average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 15 different brands of 1-ounce chocolate chip cookies resulted in the following calorie amounts. At the α = 0.01 level, is there sufficient evidence that the average calorie content is greater than 110
The average monthly cell phone bill was reported to be $50.07 by the U.S. Wireless Industry. Random sampling of a large cell phone company found the following monthly cell phone charges:At the 0.05 level of significance can it be concluded that the average phone bill has increased?Perform each of
The Old Farmer’s Almanac stated that the average consumption of water per person per day was 123 gallons. To test the hypothesis that this figure may no longer be true, a researcher randomly selected 16 people and found that they used on average 119 gallons per day and s = 5.3. At α = 0.05, is
A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained these data.At α = 0.05 can it be concluded that the average is still 5.8 visits per year? Use the P-value method.Perform each of the following
The U.S. Bureau of Labor and Statistics reported that a person between the ages of 18 and 34 has had an average of 9.2 jobs. To see if this average is correct, a researcher selected a sample of 8 workers between the ages of 18 and 34 and asked how many different places they had worked. The results
A random sample of stipends of teaching assistants in economics is listed. Is there sufficient evidence at the α = 0.05 level to conclude that the average stipend differs from $15,000? The stipends listed (in dollars) are for the academic year.
The average family size was reported as 3.18. A random sample of families in a particular school district resulted in the following family sizes:At α = 0.05, does the average family size differ from the national average?
Find the critical value (or values) for the t test for each. a. n = 10, α = 0.05, right-tailed b. n = 18, α = 0.10, two-tailed c. n = 6, α = 0.01, left-tailed d. n = 9, α = 0.025, right-tailed e. n = 15, α = 0.05, two-tailed f. n = 23, α = 0.005, left-tailed g. n = 28, α = 0.01,
Using Table F, find the P-value interval for each test value. a. t = 2.321, n = 15, right-tailed b. t = 1.945, n = 28, two-tailed c. t = -1.267, n = 8, left-tailed d. t = 1.562, n = 17, two-tailed e. t = 3.025, n = 24, right-tailed f. t = -1.145, n = 5, left-tailed g. t = 2.179, n = 13,
According to the American Pet Products Manufacturers Association, cat owners spend an average of $179 annually in routine veterinary visits. A random sample of local cat owners revealed that 10 randomly selected owners spent an average of $205 with s = $26. Is there a significant statistical
A state executive claims that the average number of acres in western Pennsylvania state parks is less than 2000 acres. A random sample of five parks is selected, and the number of acres is shown. At α = 0.01, is there enough evidence to support the claim?Perform each of the following steps.a.
The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of 2.98 minutes in length with a standard deviation of 0.98 minute. At α = 0.05 can it be concluded that the average differs from the population average? Perform each of
A survey of 15 large U.S. cities finds that the average commute time one way is 25.4 minutes. A chamber of commerce executive feels that the commute in his city is less and wants to publicize this. He randomly selects 25 commuters and finds the average is 22.1 minutes with a standard deviation of
A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at least 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At α = 0.025, is there enough evidence to reject the claim?Perform each of the following
It has been found that 85.6% of all enrolled college and university students in the United States are undergraduates. A random sample of 500 enrolled college students in a particular state revealed that 420 of them were undergraduates. Is there sufficient evidence to conclude that the proportion
The largest group of moviegoers by age is the 40- to 59-year-old age group. This group constitutes 32% of the movie-going population. A theater complex randomly surveyed the customers over a three-week period and found that out of 423 surveyed, 170 were 40 to 59 years of age. At the 0.01 level of
A survey by Men’s Health magazine stated that 14% of men said they used exercise to reduce stress. Use α = 0.10. A random sample of 100 men was selected, and 10 said that they used exercise to relieve stress. Use the P-value method to test the claim. Could the results be generalized to all adult
In the Journal of the American Dietetic Association, it was reported that 54% of kids said that they had a snack after school. A random sample of 60 kids was selected, and 36 said that they had a snack after school. Use α = 0.01 and the P-value method to test the claim. On the basis of the
The Energy Information Administration reported that 51.7% of homes in the United States were heated by natural gas. A random sample of 200 homes found that 115 were heated by natural gas. Does the evidence support the claim, or has the percentage changed? Use α = 0.05 and the P-value method. What
Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, with an enrollment of 300 students, a study found that 50 students smoked at least one pack of cigarettes a day. At α = 0.05, test the claim that 18% of all high school
According to Nielsen Media Research, of all the U.S. households that owned at least one television set, 83% had two or more sets. A local cable company canvassing the town to promote a new cable service found that of the 300 households visited, 240 had two or more television sets. At α = 0.05 is
For Americans using library services, the American Library Association (ALA) claims that 67% borrow books. A library director feels that this is not true so he randomly selects 100 borrowers and finds that 82 borrowed books. Can he show that the ALA claim is incorrect? Use α = 0.05.
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