Math 136 - Introduction to Statistics » Fall 2021 » Homework 8 Estimating the Population Mean Sigma Known

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Question #1
Find the indicated critical z value. Find the critical value zα/2zα/2 that corresponds to a 98% confidence level.
A.   2.575
B.   1.75
C.   2.05
D.   2.33
Question #2
Find the indicated critical z value. Find the value of −zα/2−zα/2 that corresponds to a confidence level of 89.48%.
A.   1.62
B.   0.0526
C.   -1.25
D.   -1.62
Question #3
Find the indicated critical z value. Find zα/2zα/2 for α=0.12α=0.12.
A.   1.175
B.   1.35
C.   2.51
D.   1.555
Question #4
Determine whether the given conditions justify using the margin of error E=zα/2∗σ/n−−√E=zα/2∗σ/n when finding a confidence interval estimate of the population mean μ. The sample size is n = 200 and σ = 19.
A.   Yes
B.   No
Question #5
Determine whether the given conditions justify using the margin of error E=zα/2∗σ/n−−√E=zα/2∗σ/n when finding a confidence interval estimate of the population mean μ. The sample size is n = 4, σ = 12.7, and the original population is normally distributed.
A.   No
B.   Yes
Question #6
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. Weights of eggs: 95% confidence;   n=53,x¯=1.34oz,σ=0.58oz.n=53,x¯=1.34oz,σ=0.58oz.
A.   0.02 oz
B.   0.16 oz
C.   0.36 oz
D.   0.13 oz
Question #7
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. College students' annual earnings: 99% confidence; n=76,x¯=$3016,σ=$872.n=76,x¯=$3016,σ=$872.
A.   $891
B.   $233
C.   $258
D.   $196
Question #8
Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. Systolic blood pressures for women aged 18-24: 94% confidence; n=92,x¯=112.1n=92,x¯=112.1 mmHg ,σ=13.5,σ=13.5 mmHg.
A.   2.6 mm Hg
B.   2.2 mm Hg
C.   2.3 mm Hg
D.   47.1 mm Hg
Question #9
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. Test scores: n = 92, x¯x¯ = 90.6, σ = 8.9; 99% confidence
A.   88.8 < μ < 92.4
B.   88.4 < μ < 92.8
C.   88.2 < μ < 93.0
D.   89.1 < μ < 92.1
Question #10
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A random sample of 105 light bulbs had a mean life of x¯=441x¯=441 hours with a standard deviation of σ=40σ=40 hours. Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type.
A.   435 hr < μ < 447 hr
B.   432 hr < μ < 450 hr
C.   431 hr < μ < 451 hr
D.   433 hr < μ < 449 hr
Question #11
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean μ.
A.   21 oz < μ < 23 oz
B.   20 oz < μ < 22 oz
C.   20 oz < μ < 23 oz
D.   19 oz < μ < 21 oz
Question #12
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A laboratory tested 83 chicken eggs and found that the mean amount of cholesterol was 233 milligrams with σ=12.9σ=12.9 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs.
A.   230 mg < μ < 236 mg
B.   229 mg < μ < 235 mg
C.   229 mg < μ < 236 mg
D.   231 mg < μ < 237 mg
Question #13
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean. A group of 66 randomly selected students have a mean score of 22.4 with a standard deviation of 2.8 on a placement test. What is the 90% confidence interval for the mean score, μ, of all students taking the test?
A.   21.8 < μ < 23.0
B.   21.6 < μ < 23.2
C.   21.7 < μ < 23.1
D.   21.5 < μ < 23.3
Question #14
Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ. Margin of error: $121, confidence level: 95%, σ = $528
A.   64
B.   74
C.   4
D.   2
Question #15
Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ. Margin of error: $126, confidence level: 99%, σ = $534
A.   105,268
B.   120
C.   69
D.   61

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