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
Dont Vape	924	478	1402
Total	1016	509	1525

Problem 1.

1. 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.

2. 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:

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.

5. 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.

6. 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.

7. Would the results of the hypothesis test change at the 1% significance level?

   Explain.

Answer 1

Problem 1:

Out of 1525 adults, 123 vape so the percent of Americans vape is

P(vape) = 123 / 1525 = 0.0807

Answer: 8.07%

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The margin of error is

Answer: 0.0137

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Problem 2:

Let sample 1 shows the sample of men and sample 2 shows the sample of women.

Conditions for inference: Number of males that vape or not vape are greater than 5. Likewise number of females that vape or not vape are greater than 5. So condition for test has been fulfilled.

Conclusion: It does not appear that “use of e-cigarettes” and “gender” are independent variables. It is not equally likely for a man to vape as it is for a woman to vape.

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Since p-value is greater than 0.01 so we fail to reject the null hypothesis at 1% level of significance That is the results of the hypothesis test would change at the 1% significance level.