Questions 1-4 are based on the following; A statistics instructor asks each student in his class to report how much the student spent on textbooks for the semester. The figures reported by students are shown below. 290 325 460 230 565 355 690 565 525 650 695 530 345 340 510 495 315 550 345 745 535 400 330 435 515 410 540 595 295 510 545 595 450 620 430 130 270 420 415 270 625 420 430 545 525 615 130 450 665 370 500 300 540 260 745 505 270 415 240 530 210 750 405 450 350 260 575 330 405 545 200 215 455 355 545 310 300 540 115 635 365 270 750 315 645 405 545 570 635 555 375 330 120 560 720 520 500 530 530 230 355 695 630 330 955 295 455 460 555 270 635 510 690 230 430 535 335 325 910 715 410 235 460 210 415 435 735 190 Treat the data above as POPULATION data. 1 The mean expenditure on textbooks by all students is: a $46044 b $46509 C $46939 d $47453 2 The variance of the expenditure on textbooks by all students is: 3133797 3032369 302246 3031927 Qnu'm The instructor takes a random sample of size n = 6 from the population data and obtains the following sample data: x 375 7'20 615 595 515 685 3 The sample mean is: $595.91 $590.01 $584.1? $578.38 mnu'm 4 The sample variance is: 13,036.81 13,823.19 14,705.52 15,6441? nnu'm 5 Ifwe take random samples of size n = 6 from this population, the number ofpossible samples is: 5,965,972,320 5,423,611,200 4,930,555,636 4,482,323,305 nnu'm 6 The expected value [mean] of sample means is equal to: a $493.70 b $484.02 c $4?4.53 d $465.23 \f'12 9-:an 13 unD'D-i :14 Dunn-Wu 15 Buns-\"n: '16 Dunn-Wu What fraction ofthe means from random samples of size 7'5 are within $25 from the population mean? 0.?898 0.8227 0.8570 0.8927 What is the margin of error for the middle interval that captures 95% ofthe sample means from samples of size 75? 43.12 41.06 39.11 37.25 The middle interval that captures 95% ofthe means from samples of size 68 is, 1233.5 1337.7 1238.3 1332.9 1242.6 1328.6 1246.5 1324.7 Suppose we double the sample size to n = 2 x 75 = 150. Regarding the impact of changing the sample size on the margin of sampling error, doubling the sample size, but keeping the error probability a at 5%, would, 29% 38% 50% 50% Decrease by Decrease by Decrease by Increase by Ifwe kept n at 7'5 but reduced the error probability to o: = 0.01, the magin of error would 20% 20% 24% 31% Decrease by Increase by Increase by Increase by 17' 9-:an 18 Elana-'51.: The middle interval that captures 99% of all means from samples ofsize ?5 is, 1234.2 1225.1 1214.5 1201.9 Now keep the error probability at o = 0.05. We want to build an interval which captures 95% of the sample means within :20 from the population mean. What is the minimum sample size that would yield such an interval? 341 322 304 287 133?.0 1346.1 1356.? 1369.3