A88 ODD ANSWERS 15. (a) H0: The distribution of prospective home buyers by the size they want their next house to be is uniform. Ha: The distribution of prospective home buyers by the size they want their next house to be is not uniform. (claim) (b) x2 0 = 5.991; Rejection region: x 2 7 5.991 (c) 10.308 (d) Reject H0. (e) There is enough evidence at the 5% level of significance to conclude that the distribution of prospective home buyers by the size they want their next house to be is not uniform. 17. (a) The expected frequencies are 17, 63, 79, 34, and 5. (b) x2 0 = 13.277; Rejection region: x 2 7 13.277 (c) 0.613 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the claim that the test scores are normally distributed. Section 10.2 (page 542) 1. Find the sum of the row and the sum of the column in which the cell is located. Find the product of these sums. Divide the product by the sample size. 3. Sample answer: For both the chi-square independence test and the chi-square goodness-of-fit test, you are testing a claim about data that are in categories. However, the chi-square goodness-of-fit test has only one data value per category, while the chi-square independence test has multiple data values per category. Both tests compare observed and expected frequencies. However, the chi-square goodness-of-fit test simply compares the distributions, whereas the chi-square independence test compares them and then draws a conclusion about the dependence or independence of the variables. 5. False. If the two variables of a chi-square independence test are dependent, then you can expect a large difference between the observed frequencies and the expected frequencies. 7. (a) – (b) Athlete has Result Stretched Not stretched Total Injury 18 (20.82) 22 (19.18) 40 No injury 211 (208.18) 189 (191.82) 400 Total 229 211 440 9. (a) – (b) Preference Bank employee New procedure Old procedure No preference Total Teller 92 (133.80) 351 (313.00) 50 (46.19) 493 Customer service representative 76 (34.20) 42 (80.00) 8 (11.81) 126 Total 168 393 58 619 11. (a) – (b) Type of car Gender Compact Full- size SUV Truck/ van Total Male 28 (28.6) 39 (39.05) 21 (22.55) 22 (19.8) 110 Female 24 (23.4) 32 (31.95) 20 (18.45) 14 (16.2) 90 Total 52 71 41 36 200 13. (a) H0: An athlete’s injury result is independent of whether or not the athlete has stretched. (claim) Ha: An athlete’s injury result is dependent on whether or not an athlete has stretched. (b) d.f. = 1; x2 0 = 6.635; Rejection region: x 2 7 6.635 (c) 0.875 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to reject the claim that an athlete’s injury result is independent of whether or not the athlete has stretched. 15. (a) H0: The result is independent of the type of treatment. Ha: The result is dependent on the type of treatment. (claim) (b) d.f. = 1; x2 0 = 2.706; Rejection region: x 2 7 2.706 (c) 12.478 (d) Reject H0. (e) There is enough evidence at the 10% level of significance to conclude that the result is dependent on the type of treatment. 17. (a) H0: The number of times former smokers tried to quit is independent of gender. Ha: The number of times former smokers tried to quit is dependent on gender. (claim) (b) d.f. = 2; x2 0 = 5.991; Rejection region: x 2 7 5.991 (c) 0.002 (d) Fail to reject H0. (e) There is not enough evidence at the 5% level of significance to conclude that the number of times former smokers tried to quit is dependent on gender. 19. (a) H0: Reasons are independent of the type of worker. Ha: Reasons are dependent on the type of worker. (claim) (b) d.f. = 2; x2 0 = 9.210; Rejection region: x 2 7 9.210 (c) 7.326 (d) Fail to reject H0. (e) There is not enough evidence at the 1% level of significance to conclude that reasons for continuing education are dependent on the type of worker. 21. (a) H0: A family’s choice to visit colleges before enrolling is independent of their income. Ha: A family’s choice to visit colleges before enrolling is dependent on their income. (claim) (b) d.f. = 6; x2 0 = 16.812; Rejection region: x 2 0 7 16.812 (c) 53.012 (d) Reject H0. (e) There is enough evidence at the 1% level of significance to conclude that a family’s choice to visit colleges before enrolling is dependent on their income.
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