review-on-testing

9 55 s 356 60 w 225 46

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Unformatted text preview: 6% in the South, and 22.5% in the West. In a random sample of 200 recent calls to a national 800- number hotline, 39 of the calls were from the Northeast, 55 from the Midwest, 60 from the South, and 46 from the West. Test at 10% level to check if the the geographical distribution of hotline callers is the same as the U.S. population distribution? Region Population Distribution 200 Callers Distribution NE 19.0% 39 MW 22.9% 55 S 35.6% 60 W 22.5% 46 Problem 1 - continued ENE=0.19(200)=38.0 EMW=0.229(200)=45.8 ES=0.356(200)=71.2 EW=0.225(200)=45.0 Region Population Distribution 200 Callers: observed counts 200 Callers: expected counts NE 19.0% 39 38 MW 22.9% 55 45.8 S 35.6% 60 71.2 W 22.5% 46 45.0 Problem 1 - continued H0: p1 = 0.19, p2 = 0.229, p3 = 0.356, p4 = 0.225 Ha: H0 fails to hold 0.19 39 38.0 0.229 55 45.8 S ( fi − Ei )2 χ =∑ Ei i=1 Ei MW 4 fi NE 2 pi 0.356 60 71.2 W 0.225 46 45.0 (39 − 38)2 (55 − 45.8)2 (60 − 71.2 )2 ( 46 − 45)2 = + + + 38 45.8 71.2 45 = 0.026 + 1.848 + 1.762 + 0.022 = 3.658 df = ( 4 − 1) = 3 Critical Value = 6.251 Do not reject the null hypothesis at the 10% level Problem 2 Approximately 13.5% of U.S. drivers are younger than age 25, with 41.4% in the 25- 44 age group, and 45.1% in the 45- and over category. For a random sample of 200 fatal accidents in her state, a safety expert _inds that 42 drivers were under 25 years old, 80 were 25- 44 years old, and 78 were at least 45 years old. At the 5% level, test whether the age distribution of drivers involved in fatal a...
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