Math 136 - Introduction to Statistics » Fall 2021 » Homework 9 Estimating Population Mean Sigma Unknown

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Question #1
Choose the one alternative that best completes the statement or answers the question. Do one of the following, as appropriate: (a) Find the critical value zα/2zα/2, (b) find the critical value tα/2tα/2, (c) state that neither the normal nor the t distribution applies. 98%; n = 7; σ = 27; population appears to be normally distributed.
A.   tα/2tα/2 = 2.575
B.   zα/2zα/2 = 2.05
C.   zα/2zα/2 = 2.33
D.   tα/2tα/2 = 1.96
Question #2
Choose the one alternative that best completes the statement or answers the question. Do one of the following, as appropriate: (a) Find the critical value zα/2zα/2, (b) find the critical value tα/2tα/2, (c) state that neither the normal nor the t distribution applies. 90%; n = 10; σ is unknown; population appears to be normally distributed
A.   tα/2tα/2 = 1.812
B.   zα/2zα/2 = 1.383
C.   tα/2tα/2 = 1.833
D.   zα/2zα/2 = 2.262
Question #3
Assume that a sample is used to estimate a population mean μ. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. 95% confidence; n = 91; x¯x¯ = 16, s = 9.1
A.   4.1
B.   1.63
C.   1.9
D.   1.71
Question #4
Assume that a sample is used to estimate a population mean μ. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. 99% confidence; n = 201; x¯x¯ = 276; s = 75
A.   16
B.   13.8
C.   10.5
D.   12.4
Question #5
Assume that a sample is used to estimate a population mean μ. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. 95% confidence; n = 12; x¯=x¯= 76.4; s = 5.9
A.   4.5
B.   3.75
C.   2.81
D.   3.38
Question #6
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. n = 10, x¯x¯= 8.7, s = 3.3, 95% confidence
A.   6.37 < μ < 11.03
B.   6.35 < μ < 11.05
C.   6.79 < μ < 10.61
D.   6.34 < μ < 11.06
Question #7
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 225 milligrams with s = 15.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
A.   214.9 mg < μ < 235.1 mg
B.   215.0 mg < μ < 235.0 mg
C.   216.9 mg < μ < 233.1 mg
D.   215.1 mg < μ < 234.9 mg
Question #8
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.
A.   $492.52 < μ < $835.76
B.   $455.65 < μ < $872.63
C.   $453.59 < μ < $874.69
D.   $493.71 < μ < $834.57
Question #9
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.2 15.5 15.9 15.5 15.0 15.7 15.0 15.7 Construct a 98% confidence interval for the mean amount of juice in all such bottles.
A.   15.77 oz < μ < 15.10 oz
B.   15.00 oz < μ < 15.87 oz
C.   15.87 oz < μ < 15.00 oz
D.   15.10 oz < μ < 15.77 oz
Question #10
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. The principal randomly selected six students to take an aptitude test. Their scores were: 76.5 85.2 77.9 83.6 71.9 88.6 Determine a 90% confidence interval for the mean score for all students.
A.   75.49 < μ < 85.74
B.   85.84 < μ < 75.39
C.   85.74 < μ < 75.49
D.   75.39 < μ < 85.84

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