A recent public opinion poll on gun control found that 60 people interviewed out of the 160 interviews supported new gun regulations.
(a) What is the point estimate for the above problem?
(b) What is the 90% confidence interval? (Use a table or SALT. Round your answers to three decimal places.)
(c) What is the 95% confidence interval? (Use a table or SALT. Round your answers to three decimal places.)
(d) Which interval is wider, the 90% confidence interval or the 95% confidence interval?
a. 90% confidence interval
b. 95% confidence interval
6. The use of the formula for margin of error requires a large sample. For each of the following combinations of n and p̂, indicate whether the sample size is large enough for use of this formula to be appropriate.
(a) n = 50 and p̂ = 0.40
The sample size is large enough.
The sample size is not large enough.
(b) n = 50 and p̂ = 0.08
The sample size is large enough.
The sample size is not large enough.
(c) n = 15 and p̂ = 0.46
The sample size is large enough.
The sample size is not large enough.
(d) n = 100 and p̂ = 0.04
The sample size is large enough.
The sample size is not large enough.
7. In a survey of 800 college students in the United States, 584 indicated that they believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action. Assuming that the sample is representative of college students in the United States, construct a 95% confidence interval for the proportion of college students who have this belief. (Use a table or SALT. Round your answers to three decimal places.)
Interpret the interval.
a. We are 95% confident that the mean number of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.
b. We are 95% confident that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls directly in the middle of this interval.
c. There is a 95% chance that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls directly in the middle of this interval.
d. There is a 95% chance that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.
e. We are 95% confident that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.
8. A newspaper infographic titled "Social Media Jeopardizing Your Job?" summarized data from a survey of 1,800 recruiters and human resource professionals. The infographic indicated that 53% of the people surveyed had reconsidered a job candidate based on his or her social media profile. Assume that the sample is representative of the population of recruiters and human resource professionals in the United States.
(a) Use the given information to estimate the proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile using a 95% confidence interval. (Use a table or SALT. Round your answers to three decimal places.)
Give an interpretation of the interval in context.
a. There is a 95% chance that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
b. We are 95% confident that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls directly in the middle of this interval.
c. We are 95% confident that the mean number of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
d. We are 95% confident that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
e. There is a 95% chance that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls directly in the middle of this interval.
Give an interpretation of the confidence level of 95%.
a. Of all possible random samples, 5% would result in an interval that includes the actual value of the population proportion.
b. Of all possible random samples, 5% would result in an interval that lies above the actual value of the population proportion.
c. Of all possible random samples, 95% would result in an interval that lies below the actual value of the population proportion.
d. Of all possible random samples, 95% would result in an interval that is centered at the actual value of the population proportion.
e. Of all possible random samples, 95% would result in an interval that includes the actual value of the population proportion.
Part B Would a 90% confidence interval be wider or narrower than the 95% confidence interval from part (a)?
a. wider
b. narrower