Statistics
4. SAT Scores The national average SAT score (for Verbal and Math) is 1028. If we assume a normal distribution with s 92, what is the 90th percentile score? What is the probability that a randomly selected score exceeds 1200?
6.2
7. Unemployment Benefits The average weekly unemployment benefit in Montana is $272. Suppose that the benefits are normally distributed with a standard deviation of $43. A random sample of 15 benefits is chosen in Montana. What is the probability that the mean for this sample is greater than the U.S. average, which is $299? Is the normal distribution appropriate here since the sample size is only 15? Explain.
6.3
8. Glass Garbage Generation A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds.
6.3
11. Home Ownership In a recent year, the rate of U.S. home ownership was 65.9%. Choose a random sample of 120 households across the United States. What is the probability that 65 to 85 (inclusive) of them live in homes that they own?
6.4
13. Health Insurance In a recent year, 56% of employers offered a consumer-directed health plan (CDHP). This type of plan typically combines a high deductible with a health savings plan. Choose 80 employers at random. What is the probability that more than 50 will offer a CDHP?
6.4
9. People Who Smoke In a recent year, 23.3% of Americans smoked cigarettes. What is the probability that in a random sample of 200 Americans, more than 50 smoke?
6.4
10. Fast-Food Bills for Drive-Thru Customers A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92. Estimate the mean bill for all cars from the drive-thru with 98% confidence
7.1
21. Monthly Gasoline Expenditures How large a sample is needed to estimate the population mean monthly gasoline expenditure within $10 with 95% confidence? The population standard deviation is $59.50.
7.1
9. Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.
7.1
11. Distance Traveled to Work A recent study of 28 randomly selected employees of a company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2.0 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 late, how much time would he suggest they allow for the commute if the average speed were 30 miles per hour?
7.2
3. Perry Como Fans Fifty-six percent of respondents to an online poll said that they were Perry Como fans. If 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are Perry Como fans? Estimate at the 95% confidence level.
7.3
7. Work Interruptions A survey found that out of a random sample 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.
7.3
4. Lifetimes of Wristwatches Find the 90% confidence interval for the variance and standard deviation for the lifetimes of inexpensive wristwatches if a random sample of 24 watches has a standard deviation of 4.8 months. Assume the variable is normally distributed. Do you feel that the lifetimes are relatively consistent?
7.4
6. Carbon Monoxide Deaths A study of generationrelated carbon monoxide deaths showed that a random sample of 6 recent years had a standard deviation of 4.1 deaths per year. Find the 99% confidence interval of the variance and standard deviation. Assume the variable is normally distributed.
7.4
1. Warming and Ice Melt The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if warming and ice melt were affecting the water level. Fifty-five measurements over a period of randomly selected weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.6. Can it be concluded at the 0.05 level of significance that the average depth has increased? Is there evidence of what caused this to happen?
8.2
20. Breaking Strength of Cable A special cable has a breaking strength of 800 pounds. The standard deviation of the population is 12 pounds. A researcher selects a random 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. Should the null hypothesis be rejected at a 0.01? Assume that the variable is normally distributed.
8.2
23. Transmission Service 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 random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use a 0.10. Do you think the a value of 0.10 is an appropriate significance level?
8.2
4. Moviegoers 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 deviation is 3.2 movies. At the 0.05 level of significance, can it be concluded that this represents a difference from the national average?
8.2
14. Internet Visits A U.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 average?
8.3
8. Cost of Braces The average cost for teeth straightening with metal braces is approximately $5400. A nationwide franchise thinks that its cost is below that figure. A random sample of 28 patients across the country had an average cost of $5250 with a standard deviation of $629. At a 0.025, can it be concluded that the mean is less than $5400?
8.3
13. After-School Snacks 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 a 0.01 and the P-value method to test the claim. On the basis of the results, should parents be concerned about their children eating a healthy snack?
8.4
7. Fans of Professional Baseball According to a professional polling company, an unbelievably low percentage—36%—of Americans said that they were fans of professional baseball. A random sample of 200 people in southwestern Pennsylvania indicated that 88 were baseball fans. At a 0.02, is the proportion greater than 36%?
8.4
11. Tornado Deaths 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 random sample of 11 years had a standard deviation of 32, is the claim believable? Use a 0.05.
8.5
7. Transferring Phone Calls 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 random sample of 15 calls is selected, and the calls are timed. The standard deviation of the sample is 1.8 minutes. At a 0.01, test the claim that the standard deviation is less than or equal to 1.2 minutes. Use the P-value method
8.5
1. First-Time Births According to the almanac, the mean age for a woman giving birth for the first time is 25.2 years. A random sample of ages of 35 professional women giving birth for the first time had a mean of 28.7 years and a standard deviation of 4.6 years. Use both a confidence interval and a hypothesis test at the 0.05 level of significance to test if the mean age of professional woman is different from 25.2 years at the time of their first birth.
8.6
19) Literacy Scores Adults aged 16 or older were assessed in three types of literacy: 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. picture on paint
9.1
7. Commuting Times The U.S. Census Bureau 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 average commuting time for the month of January was calculated for both cities. The results are shown. At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? picture on paint
9.1
1. Bestseller Books 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 weeks. At a 0.10, can we conclude that there is a difference in the mean times for the number of weeks the books were on the bestseller lists?
9.2
13. Cyber School Enrollment 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 a 0.01, is there enough evidence to support the claim that the average number of students in school districts in Allegheny County who attend cyber schools is greater than those who attend cyber schools in school districts outside Allegheny County? Give a factor that should be considered in interpreting this answer. picture on paint
9.2
2. Retention Test Scores A random sample of nonEnglish majors at a selected college was used in a study to see if the student retained more from reading a 19thcentury 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 100-point written quiz on each novel. The test results are shown. At a 0.05, can it be concluded that the book scores are higher than the DVD scores? pic on paint
9.3
9. Desire to Be Rich In a random sample of 80 Americans, 44 wished that they were rich. In a random sample of 90 Europeans, 41 wished that they were rich. At a 0.01, is there a difference in the proportions? Find the 99% confidence interval for the difference of the two proportions
9.4
10. Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 20 randomly selected areas designated as "casualty doors" was 4.1 dBA and the standard deviation of 24 randomly selected areas designated as operating theaters was 7.5 dBA. At a 0.05, can you substantiate the claim that there is a difference in the standard deviations?
9.5
2. Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find the probability that a randomly selected teacher earns a. Between $35,000 and $45,000 a year b. More than $40,000 a year c. If you were applying for a teaching position and were offered $31,000 a year, how would you feel (based on this information)?
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