Math 136 - Introduction to Statistics » Fall 2021 » Homework 7 Estimating Population Proportion_One sample

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Question #1
Find the indicated critical z value. Find the critical value zα/2 that corresponds to a 98% confidence level.
A.   2.575
B.   2.05
C.   2.33
D.   1.75
Question #2
Find the indicated critical z value. Find the value of zα/2 that corresponds to a confidence level of 94%.
A.   1.88
B.   1.96
C.   1.555
D.   2.75
Question #3
Find the indicated critical z value. Find zα/2 for α=0.08.
A.   1.41
B.   2.65
C.   1.75
D.   1.96
Question #4
Express the confidence interval using the indicated format. Express the confidence interval 0.047 < p < 0.507 in the form of p^  ± E.
A.   0.277 - 0.23
B.   0.277 ± 0.5
C.   0.277 ± 0.23
D.   0.23 ± 0.5
Question #5
Express the confidence interval using the indicated format. Express the confidence interval (0.668, 0.822) in the form of p^ ± E.
A.   0.668 ± 0.154
B.   0.745 ± 0.077
C.   0.745 ± 0.154
D.   0.668 ± 0.077
Question #6
The following confidence interval is obtained for a population proportion, p: (0.505, 0.545). Use these confidence interval limits to find the point estimate,  p^.
A.   0.525
B.   0.527
C.   0.545
D.   0.505
Question #7
The following confidence interval is obtained for a population proportion, p: 0.537 < p < 0.563. Use these confidence interval limits to find the point estimate,  p^.
A.   0.550
B.   0.537
C.   0.555
D.   0.545
Question #8
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 320, x = 60
A.   0.0385
B.   0.0428
C.   0.0514
D.   0.0449
Question #9
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 99% confidence; n = 6500, x = 1950
A.   0.0146
B.   0.00833
C.   0.0111
D.   0.0128
Question #10
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 98% confidence; the sample size is 890, of which 25% are successes
A.   0.0284
B.   0.0338
C.   0.0298
D.   0.0374
Question #11
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 51, x = 27; 95% confidence
A.   0.391 < p < 0.667
B.   0.413 < p < 0.645
C.   0.392 < p < 0.666
D.   0.414 < p < 0.644
Question #12
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 110, x = 55; 88% confidence
A.   0.422 < p < 0.578
B.   0.421 < p < 0.579
C.   0.425 < p < 0.575
D.   0.426 < p < 0.574
Question #13
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.004; confidence level: 95%; p^ and q^ unknown
A.   50,024
B.   60,018
C.   60,025
D.   60,148
Question #14
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 94%;  p^ and q^ unknown
A.   587
B.   553
C.   572
D.   486
Question #15
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.05; confidence level: 99%; from a prior study, p^ is estimated by 0.15.
A.   17
B.   407
C.   196
D.   339
Question #16
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 95%; from a prior study, p^ is estimated by the decimal equivalent of 89%.
A.   9
B.   236
C.   708
D.   209
Question #17
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.
A.   0.435 < p < 0.508
B.   0.471 < p < 0.472
C.   0.438 < p < 0.505
D.   0.444 < p < 0.500
Question #18
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate
A.   0.301 < p < 0.445
B.   0.308 < p < 0.438
C.   0.304 < p < 0.442
D.   0.316 < p < 0.430
Question #19
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. When 319 college students are randomly selected and surveyed, it is found that 120 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
A.   0.332 < p < 0.421
B.   0.323 < p < 0.429
C.   0.313 < p < 0.439
D.   0.306 < p < 0.446
Question #20
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,  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 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.
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 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

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