Question

verify that the conditions of the central limit theorem for proportions are met, giving explanations.

4) Mobile device ownership has increased dramatically in all age groups, especially among the youth market. In a recent study, 68% of teens owned a mobile telephone. In order to test this, you decide to conduct a survey of 80 random teens at a local school about mobile device ownership. a) Verify that the conditions of the Central Limit Theorem for proportions are met, giving explanations. b) Describe the sampling distribution of the proportion of teens who own a mobile telephone. (Give shape, center, and spread using symbols and formulas as necessary) c) Suppose you find that 62 of your 80-teen sample own mobile telephones, which is highly unusual with a probability of only 0.0343. Explain what three conclusions you might reach. Be specific to the context of this situation.

Answer 1

The solution to this problem is given by

solution Given data is C Samble Size = n=80 Proportions of lerson hausing mobline brone (a) since lie n sambling =6= 0.68 n6l1-P) = 8080.68(1-0.68 1704 > lo and LOON samble size is less than o equal to the 54. of bobuletion Size . @ Conditions for bodaulation So, the to proportions is satisfied Hence the diskaibution of 'B' is abproximate normal (b) The Sambling listribution is a aproximate normal with centre (mean spread (SD ) Go where repe=p .o.68 pli-b) r10 o 168(1-668) 80 0.05215 Mp and n ap

(Choi There is only 3.43% chance that that out of own mobile telephones. So only 62 will have in There chance is a A have very rare of 3.437 that Oud of so-teen samble only 62 will own mobile telephones The event is very unumad that when we take Random sample of Co 62 culll have mobile alijs will a ohen phones