500 câu trắc nghiệm Kinh tế lượng – 6A

Find the margin of error for the 95% confidence interval used to estimate the population proportion.
7) n = 163, x = 96
○ 0.0680
● 0.0755
○ 0.132
○ 0.00291

Use the given degree of confidence and sample data to construct a confidence interval for the population
proportion p.
8) n = 165, x = 138; 95 percent
○ 0.779 < p < 0.892
○ 0.791 < p < 0.881
○ 0.790 < p < 0.882
● 0.780 < p < 0.893

Find the minimum sample size you should use to assure that your estimate of \({\hat p}\) will be within the required margin of error around the population p.

Margin of error: 0.04; confidence level: 99%; from a prior study, \({\hat p}\) is estimated by 0.13
○ 563
○ 272
● 469
○ 19

Solve the problem.
10) 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.
○ 0.632
○ 0.366
○ 0.388
● 0.634

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
11) Of 139 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.
○ 15.8% < p < 27.3%
● 12.6% < p < 30.6%
○ 13.5% < p < 29.7%
○ 14.7% < p < 28.4%

Solve the problem.
12) A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the population proportion p: 0.113 < p < 0.171

Which of the statements below is a valid interpretation of this confidence interval?
A: There is a 99% chance that the true value of p lies between 0.113 and 0.171.
B: If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and 0.171.
C: If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.
D: If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value of p.
○ D
○ A
○ B
● C

Use the confidence level and sample data to find the margin of error E.
13) College students’ annual earnings: 99% confidence; n = 74, \({\bar x}\) = $3967, \(\sigma \) = $874
● $262
○ $9
○ $237
○ $1187
Use the confidence level and sample data to find a confidence interval for estimating the population \(\mu \).