A poll asked working adults about their job satisfaction. One question was \"All
ID: 3134412 • Letter: A
Question
A poll asked working adults about their job satisfaction. One question was "All in all, which best describes how you feel about your job?" The possible answers were "love job," "like job," "dislike job," and "hate job." Sixty-two percent of the sample responded that they liked their job. Results were based on telephone interviews with 1,001 adults. The poll concluded with 95% confidence that the maximum margin of sampling error is ±3 percentage points. The sample percent has approximately a Normal sampling distribution.
a.) The announced poll result was 62% ± 3%. Can we be certain that the true population percent falls in this interval? (CHOOSE ONE:)
-We cannot be certain, but we can be 95% confident.
-We can be certain because the poll question was well designed.
-We can be certain because our sample size is large.
-We can be certain because the maximum margin of sampling error is relatively small.
-We cannot be certain because the maximum margin of sampling error is relatively large.
b.) Explain to someone who knows no statistics what the announced result 62% ± 3% means. (CHOOSE ONE:)
-We obtained the interval 59% to 65% by a method that includes all individual responses 95% of the time.
-We obtained the interval 59% to 65% by a method that implies that 59% or 65% is the true mean 95% of the time.
-We obtained the interval 59% to 65% by a method that includes 95% of individual responses.
-We obtained the interval 59% to 65% by a method that includes the true mean 95% of the time.
-We obtained the interval 59% to 65% by a method that includes the sample mean 95% of the time.
c.) This confidence interval has the same form we have met earlier: estimate ± z*estimate
What is the standard deviation estimate of the estimated percent? (Round your answer to one decimal place.)
d.) Does the announced margin of error include errors due to practical problems such as undercoverage and nonresponse? (CHOOSE ONE:)
-No, confidence intervals only account for random sampling error.
-Yes, confidence intervals account for all error, including nonresponse and undercoverage.
-No, confidence intervals do not account for error due to nonresponse or undercoverage. They do account for error due to other practical problems.
-No, confidence intervals do not account for error due to nonresponse. They do account for undercoverage.
-No, confidence intervals do not account for error due to undercoverage. They do account for nonresponse.
Explanation / Answer
a.) The announced poll result was 62% ± 3%. Can we be certain that the true population percent falls in this interval? (CHOOSE ONE:)
-We cannot be certain, but we can be 95% confident.
b.) Explain to someone who knows no statistics what the announced result 62% ± 3% means. (CHOOSE ONE:)
-We obtained the interval 59% to 65% by a method that includes the true mean 95% of the time.
c.) This confidence interval has the same form we have met earlier: estimate ± z*estimate
What is the standard deviation estimate of the estimated percent? (Round your answer to one decimal place.)
alpha = 0.05 alpha / 2 = 0.025 Z= 1.96
0.03 = 1.96 * SD / srqt(1001)
SD = 0.4843
d.) Does the announced margin of error include errors due to practical problems such as undercoverage and nonresponse? (CHOOSE ONE:)
-No, confidence intervals do not account for error due to nonresponse or undercoverage. They do account for error due to other practical problems.