Question

My Notes The report titled "Digital Democracy Survey stated that 31% of the people in a representative sample of adult Americans age 33 to 49 rated a landine telephone among the three most important services that they purchase for their home in a representative sample of adult Americans age 50 to 68, 48% rated a landine telephone as one of the top three services they purchase for their home. Suppose that the samples were independently selected and that the sample site was 600 for the 33 to 49 age group sample and 650 for the 50 to 68 age group sample. Does this data provide convincing evidence that the proportion of adult Americans age 33 to 49 who rate a landline phone in the top three is less than this proportion for adult Americans age 50 to 7 Test the relevant hypotheses using 0.05. (Let P, be the proportion of adult Americans ages 3 to 49 who rate a landine phone in the top three, and be the proportion of adult Americans ages so to 68 who rate a landline phone in the top three) State the appropriate null and alternative wypotheses Hol PPO HiPP > 0 Holm-P₂ JO HiPP20 O HOIR-P20 HP1 P2 > 0 O HORI-P2 = 0 HaiPo-P20 Ho: P.-P2-0 H, P1-P2co

Answer 1

$ = 0. 3, 6, = 0. 4-8 ni = 600, n2 = 650 ** Ho : Po-P2 = 0 Hai Pi - Pz co z. - TBC-B3) + B 11- B2) ** Z = nz 0.31–0.48 10.31(1-0.31), 0:48(1-0:48) J 600 650 - 6.2472 16.25 Co ** P-value = 0.00000 x10.0000 ** option (iv): we Reject Ho. We have convincing evidence that the proportion of adult Americans age 33 to 49 who rate a landline phone in the top three is less than this proportion for adult Americans age 50 to 68.