Select one: a. The 80% confidence level has a confidence interval length of 20.5

Question

Select one:

a. The 80% confidence level has a confidence interval length of 20.5; the 90% confidence level has a confidence interval length of 26.4; and the 95% confidence level has a confidence interval length of 31.5. As the confidence level increases, the confidence interval lengths increases.

b. The 80% confidence level has a confidence interval length of 106.8; the 90% confidence level has a confidence interval length of 137.2; and the 95% confidence level has a confidence interval length of 163.5. As the confidence level increases, the confidence interval length increases.

c. The 80% confidence level has a confidence interval length of 4.0; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 6.1. As the confidence level increases, the confidence interval lengths increases.

d. The 80% confidence level has a confidence interval length of 163.5; the 90% confidence level has a confidence interval length of 137.2; and the 95% confidence level has a confidence interval length of 106.8. As the confidence level increases, the confidence interval lengths decreases.

e. The 80% confidence level has a confidence interval length of 6.1; the 90% confidence level has a confidence interval length of 5.1; and the 95% confidence level has a confidence interval length of 4.0. As the confidence level increases, the confidence interval length decreases.

Explanation / Answer

80% confidence level z value = 1.28

90% z = 1.64

100% z = 1.96

Hence as confidence level increses intervals increase in length.

Margin of error = 1.28 sigma, 1.64 sigma and 1.96 sigma.

Hence length of conf interval will be proportional to 128, 164 , 196

Or in the ratio 32:41:49

In a) 20.5: 26.4:31.5 = 32:64:76

Not in the same ratio hence rejected

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b) 106.8, 137.2,163.5 are in the ratio with first one 32 is

32:41:49

Hence option b is right answer

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c) conf interval incresaes and ratios are 4:5.1:6.1 = 32:40.8:48.8

Almost equal to 32:41:49. This also is true with a slight difference

d and e need not be checked as decresaes is wrong.

Hence option b and c

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