Question

In: Math

Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey...

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: State the null and alternative hypotheses. Be sure to include proper statistical notation. Check the conditions for inference. Compute the test statistic. For full credit, be sure to show your work. 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. 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. 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. Would the results of the hypothesis test change at the 1% significance level? Explain.

Solutions

Expert Solution

Problem 1:

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

P(vape) = 123 / 1525 = 0.0807

Answer: 8.07%

----------------------------------------------------

The margin of error is

Answer: 0.0137

--------------------------------------------------

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.

-----------------

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.


Related Solutions

Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The survey...
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...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The following...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The following example is based on hypothetical data that is meant to be similar to the data collected by Gallup. The following table considers survey data about annual household income and whether or not a person vapes. <$35,000 $35,000-$99,999 $100,000+ Total Vape 47 57 19 123 Do Not Vape 381 659 362 1402 Total 428 716 381 1525 Problem 1. Based on recent data, about 28%...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The following...
Gallup recently conducted a survey about the proportion of Americans who use e-cigarettes (vape). The following example is based on hypothetical data that is meant to be similar to the data collected by Gallup. The following table considers survey data about annual household income and whether or not a person vapes. <$35,000 $35,000-$99,999 $100,000+ Total Vape 47 57 19 123 Do Not Vape 381 659 362 1402 Total 428 716 381 1525 Problem 1. Based on recent data, about 28%...
A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 387 women...
A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 387 women and 359 men were independently and randomly selected, and that 242 women and 202 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women (p1), choosing the state of the economy as their biggest concern, exceeds the proportion of men (p2)?  Use a significance level of α=0.01 for the test. Step 1: Choose the correct alternative...
Question 1: A survey was conducted to estimate the proportion of car drivers who use seatbelts...
Question 1: A survey was conducted to estimate the proportion of car drivers who use seatbelts while driving. Of the 1500 drivers sampled, 520 drivers said, they always use seatbelt while driving. - Estimate the value of the population proportion. - Compute the standard error of the proportion. - Develop a 99% confidence interval for the population proportion. - Interpret your findings Question 2: The registrar wants to estimate the arithmetic mean of grade point average (GPA) of all graduating...
According to a study conducted by a statistical organization, the proportion of Americans who are satisfied...
According to a study conducted by a statistical organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.66. Suppose that a random sample of 205 Americans is obtained, a. About 69% of the samples will contain more than x Americans who are satisfied with their lives. Find the x. b. What is the probability that at least 140 Americans in the sample are satisfied with their lives? c. What is the...
According to a study conducted by a statistical​ organization, the proportion of Americans who are satisfied...
According to a study conducted by a statistical​ organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.76. Suppose that a random sample of 110 Americans is obtained. Complete parts​ (a) through​ (c). (a) Describe the sampling distribution of p. (b) Using the distribution from part​ (a), what is the probability that at least 80 Americans in the sample are satisfied with their​ lives? (c) Using the distribution from part​ (a),...
Label and circle/underline answer. Please show work correctly. Gallup recently conducted a surveyabout the proportion of...
Label and circle/underline answer. Please show work correctly. Gallup recently conducted a surveyabout the proportion of Americans who use e-cigarettes (vape). The following example is based on hypothetical data that is meant to be similar to the data collected by Gallup. The following table considers survey data about annual household income and whether or not a person vapes. <$35,000 $35,000-$99,999 $100,000+ Total Vape 47 57 19 123 Do Not Vape 381 659 362 1402 Total 428 716 381 1525 Problem...
Label and circle/underline answer. Please show work correctly. Gallup recently conducted a surveyabout the proportion of...
Label and circle/underline answer. Please show work correctly. Gallup recently conducted a surveyabout the proportion of Americans who use e-cigarettes (vape). The following example is based on hypothetical data that is meant to be similar to the data collected by Gallup. The following table considers survey data about annual household income and whether or not a person vapes. <$35,000 $35,000-$99,999 $100,000+ Total Vape 47 57 19 123 Do Not Vape 381 659 362 1402 Total 428 716 381 1525 Problem...
12-According to a study conducted by a statistical organization, the proportion of Americans who are satisfied...
12-According to a study conducted by a statistical organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.66. Suppose that a random sample of 205 Americans is obtained, -About 69% of the samples will contain more than x Americans who are satisfied with their lives. Find the x. -What is the probability that at least 140 Americans in the sample are satisfied with their lives? -What is the probability that 157...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT