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 92 31 Vape Do Not Vape Total 478 924 1016 Total 123 1402 1525 509 1 Problem 1. a. (1 point) Based on the data found in the table, approximately what percent of Americans vape? For credit, be sure to show your work. Round to two digits after the decimal. b. (3 points) What is the margin of error of this estimate? Use a 95% confidence level and be sure to show your work with an appropriate sketch. Round to four digits after the decimal. 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: a. (2 points) State the null and alternative hypotheses. Be sure to include proper statistical notation. b. (3 points) Check the conditions for inference, c. (2 points) Compute the test statistic. For full credit, be sure to show your work d. (2 points) 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. e. (2 points) Using either the p-value or critical value method, make a decision about the null hypothesis. Be sure to show how your decision was made. f. (1 point) Based on the results of the hypothesis test, does it appear that "use of e- cigarettes" and "gender" are independent variables? In other words, is it equally likely for a man to vape as it is for a woman to vape? Explain. 8. (2 points) Would the results of the hypothesis test change at the 1% significance level? Explain.

Answer 1

P900-1 Solutions adults living 50 us stater Gelven data : → random sample of 1595 → Minimum quota of 70% + Cellphone respondents 30% landline Men Women Total Vape 31 123 Do not vape 924 478 140 Total 1016 509 155 ->total bize = 1525 Number & people dape = 123 percentage of American Vape = No. of people lape size sub, The values in a formula = 15.25 = 0.0806 . at should be a . keep - a percentage

-8.07% Pgnola La percentage of American Vape = 8.07% XE005 => 95% confidence heiet = 0.05, z = " → Morgen er 6 = 2 * $($+(1-5)/n) 7 -0.05 7=1196 whole, 21.96 = 1525 - >0.9193 , p = 0.0807 36, F = 1.96 * (0.0807 *0.993)|1585) = 1,96 0.00697 = 0.0137 -0.0137

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