Question

Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey data was collected via random-digit-dial telephone interviews conducted July 1-12, 2019 with a random sample of 1525 adults living in all 50 U.S. states with a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. The following table summarizes their results for men and women:

	Men	Women	Total
Vape	92	31	123
Do Not Vape	924	478	1402
Total	1016	509	1525

Problem 2. Does the data suggest that a greater proportion of men vape compared to women? Conduct a hypothesis test to at the 5% significance level by completing the following steps:

1. State the null and alternative hypotheses. Be sure to include proper statistical notation.
2. Check the conditions for inference.
3. Compute the test statistic. For full credit, be sure to show your work.
4. Determine the p-value or the critical value (depending on the method you prefer). Either way, be sure to show your work by drawing a sketch.

Answer 1

HO Assume that their is no greater proportion of men vape compared to women. Assume that their is greater proportion of men vape compared to wonnen. Here we can use chi sanare test Test statistic x? Ž { coi; - Eis) Eij x - chi square test independence Oij = observed frequency E;;= expected frequency men vape 92 women Total 478 1402 924 Do not vape Total sog 1525 to 16 P (Group I and Responce 1) = P(Group 1 x P (resonce ! - (123/1525x(1016/1525) -

0.0537 Similarly calculate another group also. cal x = 4,020 = (2-1) × (2-1) = 1 Herre D.F= (N-1) & (C-1) where s- so of cows. & a- no of columns gunog 3.8414 2 Tabulated value X (-1) (C-1) 62 = 0.025 - Pvtwo • o40 2 Here pralul a = 0.015 so we reject the at s t level of significance conclusion - assume that their is greater proportion of men vape compared to women.