hw6 - -W Dr an on wail/ti ”Pastime EXEI‘CiSBS(53 A...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -W Dr; an on wail/ti ”Pastime EXEI‘CiSBS (53 A chain of department stores is interested in estimating the proportion of accounts re~ ceivable that are delinquent. The chain consists of four stores. So that the cost of sarnw pling is reduced, stratified random sampiing is used, with each store as a stratum. Because no information on population proportions is availabie before sampling, propor- tionai aiiocation is used. From the accompanying tabie, estimate p, the proportion of delinquent accounts for the chain, and piace a bound on the error of estimation. Stratum Stratum Stratum Stratum I II III IV Number of N1 2 65 N2 = 42 N3 = 93 N4 : 25 accounts receivable Sample size n1 2 14 17.2 m 9 723 m 21 R4 = 5 Sample number or" 4 2 8 i deiinquent accounts @ A corporation desires to estimate the total number of worker-hours lost for a given month because of accidents among alt employees. Because laborers, technicians, and adminism trators have different accident rates, the researcher decides to use stratified random sam- pling, with each group forming a separate stratum. Data from previous years suggest the variances shown in the accompanying table for the number of worker~hours lost per employee in the three groups, and current data give the stratum sizes. Determine the Neyrnan allocation for a sample of n = 30 employees. 1 I] III 2 ) (laborers) (technicians) (administrators) <5" )3 W 2 _ 2 ._ 2 _ o“ —_ 36 :72 — 25 (73 m SZPA 5% W, N12132 N2 m 92 N3 w.» 27 uncut .. . . . . _ For Exerczse 5.2, estimate the total number of worker-hours lost during the given month and place a bound on the error of estimation. Use the data in the accompanying table, ob tained from sampiing 18 laborers, 10 technicians, and 2 administrators. Make a plot of the data to check for unusual features. I II III (laborers) (technicians) (administrators) 8 4 1 24 0 8 G 8 G 3 16 1 32 5 24 12 l 2 S omgwmmeeqmoo‘ .A report from the Census Bureau in October 1994 provided data on new one«family houses for a sample of 28 metropolitan statistical areas (MSAS) and consolidated metro- politan statistical areas (CMSAs) from around the country. {CMSAs tend to be larger than MSAS and can be subdivided into other metropolitan areas for purposes of census data summaries.) Data on total housing units sotd, median sales price, and median floor area per house are reported, as shown in the table. The median sales price can be thought of as a typieai price for that area. Similarly, the median floor area can be thought of as a typical floor area for houses in that area. There were 250 MSAs and 18 CMSAs in the United States for the year in which these data were reported. a. Plot the sales prices in parallel box plots, one for MSAs and one for CMSAS, and comment on any unusual features you see. Do you see any reason to make adjustments to the data before proceeding to estimate the mean typical selling price for the country? I). Treating these data as a stratified random sample, with the MSAS and CMSAs being the two strata, estimate the mean typical sales price per house for all metropolitan areas of the United States. Calculate a bound for the error of estimation. c. Ptot the total number of units sold in parallel box plots, one for each stratum. Do you see any unusual features here? (1. Estimate the totai number of houses sold in alt metropolitan areas of the United States in 1993 and calculate a bound for the error of estimation. e. Suppose you are to estimate the population mean or total for each of the three vari- ables in the data set. For which of the three outcome variablesutotal units sold, price, or square footage—will stratification produce the least gain in precision over simple random sampling? Explain. ' , f. Estimate the difference in average typical selling price betwoen the two strata. Can we‘ say that houses in the CMSAs are, on the average, higher priced than those in the MSAs? Median 1993 Sales Finished total sold price floor area Metmpolitan area (thousands) (doliars) {square feet) Atlanta, GA MSA 27.8 $118,200 2120 Charlotte-Gastonia-Rock Hill, NC~SC MSA 7.8 115,100 1945 Chicago—Garwaenosha, lL—IN—WI CMSA 18.9 159,500 2020 Colorado Springs. CO MSA 3.0 138,600 2210 Dallas—Fort Worth,TX CMSA 19.2 _ 123,000 2325 Denver-B oulderwGreeiey, CO CMSA 11.9 174,600 2225 Houston—Galveston—Brazoria,TX CMSA 10.2 114,200 2680 Jacksonville, FL MSA 5.0 95,000 1995 Kansas City, MOwKS MSA 6.5 99,300 1720 Las Vegas, NV-AZ MSA 18.5 121,700 1770 Los Angeles-Riverside-Orange County, CA CMSA 23,4 139,800 1820 Miami—Fort Lauderdale, FL CMSA 11.2 131,500 2185 Minneapolis-St. Paul, MN-Wl MSA 10.6 155,600 2030 New Orleans, LA MSA , 1.6 99,200 2045 New York—Northern NJwLong Isiand, NY—NJ—CT—PA CMSA 17.9 191,400 2140 Norfolk-Virginia Beach-NeWport News, VA—NC MSA 6.0 120,200 2245 Orlando, FL MSA 10.5 107,500 1725 Phoenix—Mesa, AZ MSA 21.9 113,900 2180 Sacramento—Yule, CA CMSA 6.5 144,000 1540 St. Louis, MO—lL MSA 6.9' 144,500 1995 Salt Lake City-Ogden, UT MSA 6.5 100,300 1545 San Antonio,’1‘X'MSA 3.0 117,900 2375 San Diego, CA MSA 3.8 225,000 2375 Seattle-Tacoma—Bremertou, WA CMSA 10.8 159,700 1885 Tampa-St. PetersburgClearwatcr, FL MSA 8.4 113,700 2240 Tucson, AZ MSA 3.8 106,600 1810 Washington—Baitirnore, DC—MD‘VA—WV CMSA 31.1 184,400 2305 West Palm Beach—Boea Raton, FL MSA 5.6 158,400 250 @ Acorporation wishes to obtain information on the effectiveness of a business machine. A number of division heads will he interviewed by telephone and asked to rate the equip ment on a numerical scaie. The divisions are located in North America, Europe, and Asia. Hence, stratified sampling is used. The costs are larger for interviewing division heads loéated outside North America. The accompanying table gives the costs per interview, approximate variances of the ratings, and N that have been established. rl‘he corporation wants to estimate the average rating with V075,) : 0.]. Choose the sample size n that achieves this bound, and find the appropriate allocation. Stratum I Stratum II Stratum III (N orth America) (Europe) (Asia) c; 2 $9 c; 2 $25 C3 = $36 a”? = 2.25 0% :2 3.24 a; m 3.24 N;=:112 N2=6S 513239 A school desires to estimate the average score that may be obtained on a reading com— prehension exam for students in the sixth grade. The school’s students are grouped into three tracks, with the fast learners in track I and the slow learners in track HI. The school decides to stratify on tracks because this method should reduce the variability of test scores. The sixth grade contains 55 students in track I, 80 in track II, and 65 in track III. A stratified random sample of 50 students is proportionally allocated and yields simple random samples of m z 14, n; m 20, and :23 = 16 from tracks I, II, and III. The test is administered to the sample of students, With the results as shown in the table. a. Estimate the average score for the sixth grade, and place a bound on the error of esti- mation. Track I Track 11 Track III so 85 42 92 32 32 68 48 36 as 75 31 72 53 65 87 73 29 85 65 43 91 7s 19 9o 49 53 31 69 14 52 72 61 79 81 31 6t 53 42 33 59 30 as 39 52 32 71 ' 61 59 42 WW 1). Construct parallel box plots for these data and comment on the patterns you see. Do you think there could be a problem in placing students in tracks? c. Estimate the difference in average scores between track I and track II students. Are Suppose the average test score for the class in track I students significantly better, on the average, than traclc 13 students? (3 Exercise 5.6 is to be estimated again at the pling are equal in all strata, Iout the variances dif— fer. Find the optimum (Neyman) allocation of a sample of size 50, using the data in Ex- ercise 5.6 to approximate the variances. a score, With a bound of four points on the error of estimation. Use proportional allocation. 5 .9 Repeat Exercise 5.8 using Neyman allocatio It. Compare the results with the answer to Exercise 5.8. ‘ ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern