Assignment 3 Qs 1) Table below shows the data. Let’s assume that the population standard deviation of all such prices is $7.2 thousand, that is, $7200. a. Identify the distribution of the variable x¯, that is, the sampling distribution of the sample mean for samples of size 36. b. Use part (a) to show that 95.44% of all samples of 36 new mobile homes have the property that the interval from x¯ − 2.4 to x¯ + 2.4 contains μ. c. Use part (b) and the sample data in Table 8.1 to find a 95.44% confidence interval for μ, that is, an interval of numbers that we can be 95.44% confident contains μ Qs 2) A simple random sample of 35 new models yielded the following data on fuel tank capacity, in gallons. a. Find a point estimate for the mean fuel tank capacity of all new automobile models. Interpret your answer in words. (Note: xi = 664.9 gallons.) b. Determine a 95.44% confidence interval for the mean fuel tank capacity of all new automobile models. Assume σ = 3.50 gallons. Qs 3) A random sample of 18 venture capital investments in the fiber optics business sector yielded the following data, in millions of dollars. a. Determine a 95% confidence interval for the mean amount, μ, of all venture-capital investments in the fiber optics business sector. Assume that the population standard deviation is $2.04 million. (Note: The sum of the data is $113.97 million.) b. Interpret your answer from part (a). Qs 4) A sample of 87 professional working women showed that the average amount paid annually into a private pension fund per person was $3352. The population standard deviation is $1100. A sample of 76 professional working men showed that the average amount paid annually into a private pension fund per person was $5727, with a population standard deviation of $1700. A women’s activist group wants to “prove” that women do not pay as much per year as men into private pension funds. If they use = .001 and these sample data, will they be able to reject a null hypothesis that women annually pay the same as or more than men into private pension funds? Use the eight-step hypothesis-testing process Qs 5) A consumer test group wants to determine the difference in gasoline mileage of cars using regular unleaded gas and cars using premium unleaded gas. Researchers for the group divided a fleet of 100 cars of the same make in half and tested each car on one tank of gas. Fifty of the cars were filled with regular unleaded gas and 50 were filled with premium unleaded gas. The sample average for the regular gasoline group was 21.45 miles per gallon (mpg), and the sample average for the premium gasoline group was 24.6 mpg. Assume that the population standard deviation of the regular unleaded gas population is 3.46 mpg, and that the population standard deviation of the premium unleaded gas population is 2.99 mpg. Construct a 95% confidence interval to estimate the difference in the mean gas mileage between the cars using regular gasoline and the cars using premium gasoline Qs 6) Examine the following data. Assume the variances for the two populations are 22.74 and 26.65 respectively. a. Use the data to test the following hypotheses ( = .02). b. Construct a 98% confidence interval to estimate the difference in population means using these data. How does your result validate the decision you reached in part (a)? Qs 7) Suppose that for years the mean of population 1 has been accepted to be the same as the mean of population 2, but that now population 1 is believed to have a greater mean than population 2. Letting = .05 and assuming the populations have equal variances and x is approximately normally distributed, use the following data to test this belief Qs 8) According to an Experiential Education Survey published at JobWeb.com, the average hourly wage of a college student working as a co-op is $15.64 an hour and the average hourly wage of an intern is $15.44. Assume that such wages are normally distributed in the population and that the population variances are equal. Suppose these figures were actually obtained from the data below. a. Use these data and to test to determine if there is a significant difference in the mean hourly wage of a college co-op student and the mean hourly wage of an intern. b. Using these same data, construct a 90% confidence interval to estimate the difference in the population mean hourly wages of co-ops and interns. Qs 9) Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings of the 11 employees both before the new diet and one month after use of the diet began. Construct a 98% confidence interval to estimate the population mean difference of cholesterol readings for people who are involved in this program. Assume differences in cholesterol readings are normally distributed in the population Qs 10) According to a study conducted for Gateway Computers, 59% of men and 70% of women say that weight is an extremely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/very important factor in purchasing a laptop computer? Use a 5% level of significance. Qs 11) A large production facility uses two machines to produce a key part for its main product. Inspectors have expressed concern about the quality of the finished product. Quality control investigation has revealed that the key part made by the two machines is defective at times. The inspectors randomly sampled 35 units of the key part from each machine. Of those produced by machine A, five were defective. Seven of the 35 sampled parts from machine B were defective. The production manager is interested in estimating the difference in proportions of the populations of parts that are defective between machine A and machine B. From the sample information, compute a 98% confidence interval for this difference Qs 12) A total of 603 interviews were conducted among a national sample of adults with household incomes of at least $150,000. Of the adults interviewed, 410 said they had purchased clothing, accessories, or books online in the past year. Find a 95% confidence interval for the proportion of all U.S. adults with household incomes of at least $150,000 who purchased clothing, accessories, or books online in the past year. Qs 13) Suppose the data shown here are the results of a survey to investigate gasoline prices. Ten service stations were selected randomly in each of two cities and the figures represent the prices of a gallon of unleaded regular gasoline on a given day. Use the F test to determine whether there is a significant difference in the variances of the prices of unleaded regular gasoline between these two cities. Let Assume gasoline prices are normally distributed Qs 14) The Higher Education Research Institute of the University of California, Los Angeles, publishes information on characteristics of incoming college freshmen in The American Freshman. In 2000, 27.7% of incoming freshmen characterized their political views as liberal, 51.9% as moderate, and 20.4% as conservative. For this year, a random sample of 500 incoming college freshmen yielded the preceding frequency distribution for political views. a. Identify the population and variable under consideration here. b. At the 5% significance level, do the data provide sufficient evidence to conclude that this year’s distribution of political views for incoming college freshmen has changed from the 2000 distribution? c. Repeat part (b), using a significance level of 10% Qs 15) March 4, 2009, was one of the few good days for the stock market in early 2009. The Dow Jones Industrial Average went up 149.82 points (The Wall Street Journal, March 5, 2009). The following table shows the stock price changes for a sample of 12 companies on that day. a. Compute the sample variance for the daily price change. b. Compute the sample standard deviation for the price change. c. Provide 95% confidence interval estimates of the population variance and the population standard deviation. Qs 16) The Japan Automobile Manufacturer’s Association provides data on exported vehicles in Japan’s Motor Vehicle Statistics, Total Exports by Year. In 2005, cars, trucks, and buses constituted 86.4%, 12.1%, and 1.5% of vehicle exports, respectively. This year, a simple random sample of 750 vehicle exports yielded 665 cars, 71 trucks, and 14 buses. a. At the 5% significance level, do the data provide sufficient evidence to conclude that this year’s distribution for exported vehicles differs from the 2005 distribution? b. Repeat part (a) at the 10% significance level. Qs 17) What is the first big change that American drivers made due to higher gas prices? According to an Access America survey, 30% said that it was cutting recreational driving. However, 27% said that it was consolidating or reducing errands. If these figures are true for all American drivers, and if 20 such drivers are randomly sampled and asked what is the first big change they made due to higher gas prices, a. What is the probability that exactly 8 said that it was consolidating or reducing errands? b. What is the probability that none of them said that it was cutting recreational driving? c. What is the probability that more than 7 said that it was cutting recreational driving? Qs 18) An increasing number of consumers believe they have to look out for themselves in the marketplace. According to a survey conducted by the Yankelovich Partners for USA WEEKEND magazine, 60% of all consumers have called an 800 or 900 telephone number for information about some product. Suppose a random sample of 25 consumers is contacted and interviewed about their buying habits. a. What is the probability that 15 or more of these consumers have called an 800 or 900 telephone number for information about some product? b. What is the probability that more than 20 of these consumers have called an 800 or 900 telephone number for information about some product? c. What is the probability that fewer than 10 of these consumers have called an 800 or 900 telephone number for information about some product? Qs 19) A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distributed. a. What is the probability of selecting a carton and finding no defective pens? b. What is the probability of finding eight or more defective pens in a carton? c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than three defective pens. What is the probability that a carton contains more than three defective pens? Qs 20) A data firm records a large amount of data. Historically, .9% of the pages of data recorded by the firm contain errors. If 200 pages of data are randomly selected, a. What is the probability that six or more pages contain errors? b. What is the probability that more than 10 pages contain errors? c. What is the probability that none of the pages contain errors? d. What is the probability that fewer than five pages contain errors? Qs 21) The average number of annual trips per family to amusement parks in the United States is Poisson distributed, with a mean of 0.6 trips per year. What is the probability of randomly selecting an American family and finding the following? a. The family did not make a trip to an amusement park last year. b. The family took exactly one trip to an amusement park last year. c. The family took two or more trips to amusement parks last year. d. The family took three or fewer trips to amusement parks over a three-year period. e. The family took exactly four trips to amusement parks during a six-year period. Qs 22) A consumer test group wants to determine the difference in gasoline mileage of cars using regular unleaded gas and cars using premium unleaded gas. Researchers for the group divided a fleet of 100 cars of the same make in half and tested each car on one tank of gas. Fifty of the cars were filled with regular unleaded gas and 50 were filled with premium unleaded gas. The sample average for the regular gasoline group was 21.45 miles per gallon (mpg), and the sample average for the premium gasoline group was 24.6 mpg. Assume that the population standard deviation of the regular unleaded gas population is 3.46 mpg, and that the population standard deviation of the premium unleaded gas population is 2.99 mpg. Construct a 95% confidence interval to estimate the difference in the mean gas mileage between the cars using regular gasoline and the cars using premium gasoline. Qs 23) Use the following sample information to construct a 90% confidence interval for the difference in the two population means. Qs 24) Use the following contingency table and the chi-square test of independence to determine whether social class is independent of number of children in a family. Qs 25) Is the transportation mode used to ship goods independent of type of industry? Suppose the following contingency table represents frequency counts of types of transportation used by the publishing and the computer hardware industries. Analyze the data by using the chi-square test of independence to determine whether type of industry is independent of transportation mode. Let level of significance = 0.05. Qs 26) Is the number of children that a college student currently has independent of the type of college or university being attended? Suppose students were randomly selected from three types of colleges and universities and the data shown represent the results of a survey of those students. Use a chisquare test of independence of answer the question. Let level of significance = 0.05.
