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.   1.75
B.   2.05
C.   2.33
D.   2.575
Question #2
Find the indicated critical z value. Find the value of zα/2 that corresponds to a confidence level of 94%.
A.   1.555
B.   2.75
C.   1.88
D.   1.96
Question #3
Find the indicated critical z value. Find zα/2 for α=0.08.
A.   1.96
B.   2.65
C.   1.75
D.   1.41
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 - 0.23
C.   0.23 ± 0.5
D.   0.277 ± 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.   0.745 ± 0.077
B.   0.668 ± 0.077
C.   0.745 ± 0.154
D.   0.668 ± 0.154
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.   0.527
B.   0.505
C.   0.545
D.   0.525
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.   0.555
C.   0.545
D.   0.537
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.   0.0428
B.   0.0385
C.   0.0449
D.   0.0514
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.   0.0111
B.   0.0128
C.   0.00833
D.   0.0146
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.   0.0338
B.   0.0298
C.   0.0284
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.   0.392 < p < 0.666
B.   0.414 < p < 0.644
C.   0.391 < p < 0.667
D.   0.413 < p < 0.645
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.   0.425 < p < 0.575
C.   0.426 < p < 0.574
D.   0.421 < p < 0.579
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.   60,025
B.   60,018
C.   50,024
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.   553
B.   572
C.   486
D.   587
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.   196
C.   339
D.   407
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.   708
C.   209
D.   236
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.   0.444 < p < 0.500
B.   0.471 < p < 0.472
C.   0.438 < p < 0.505
D.   0.435 < p < 0.508
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.   0.308 < p < 0.438
B.   0.301 < p < 0.445
C.   0.316 < p < 0.430
D.   0.304 < p < 0.442
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.   0.323 < p < 0.429
B.   0.313 < p < 0.439
C.   0.332 < p < 0.421
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 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.

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