Math 136 - Introduction to Statistics » Fall 2021 » Homework 10 Estimating Population Standard Deviation and Variance

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Question #1
Find the critical value x2RxR2 corresponding to a sample size of 3 and a confidence level of 95 percent.
A.   7.378
B.   0.0506
C.   5.991
D.   0.103
Question #2
Find the critical value x2RxR2 corresponding to a sample size of 5 and a confidence level of 98 percent
A.   0.297
B.   11.143
C.   13.277
D.   0.484
Question #3
Find the chi-square value x2RxR2  corresponding to a sample size of 17 and a confidence level of 98 percent.
A.   32
B.   28.845
C.   5.812
D.   6.908
Question #4
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. Weights of men: 90% confidence; n = 14, x¯¯¯x¯ = 161.0 lb, s = 10.9 lb
A.   8.3 lb < σ < 16.2 lb
B.   8.8 lb < σ < 2.7 lb
C.   8.1 lb < σ < 15.3 lb
D.   8.6 lb < σ < 14.1 lb
Question #5
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. The mean replacement time for a random sample of 20 washing machines is 9.4 years and the standard deviation is 2.6 years. Construct a 99% confidence interval for the standard deviation, σ, of the replacement times of all washing machines of this type.
A.   1.8 yr < σ < 4.9 yr
B.   1.8 yr < σ < 4.3 yr
C.   1.8 yr < σ < 5.5 yr
D.   1.9 yr < σ < 4.1 yr
Question #6
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place than is used for the original set of data. The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: 9 5 7 12 14 14 5 11 6 9 Find a 95% confidence interval for the population standard deviation σ.
A.   2.4 min < σ < 6.3 min
B.   2.4 min < σ < 5.8 min
C.   2.3 min < σ < 5.8 min
D.   0.7 min < σ < 2.2 min
Question #7
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place than is used for the original set of data. The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.9 15.2 15.3 15.2 15.3 15.8 15.1 15.2 Find a 98% confidence interval for the population standard deviation σ.
A.   0.18 oz < σ < 0.62 oz
B.   0.19 oz < σ < 0.62 oz
C.   0.21 oz < σ < 0.80 oz
D.   0.19 oz < σ < 0.72 oz
Question #8
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects.
A.   17.2 < σ < 27.2
B.   16.6 < σ < 28.6
C.   16.9 < σ < 29.3
D.   17.5 < σ < 27.8

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