Do one of the following, as appropriate: (a) Find the critical value za/2, (b) f

Question

Do one of the following, as appropriate: (a) Find the critical value za/2, (b) find the critical value ta/2, (c) state that neither the normal nor the t distribution applies. 8) 98%; n = 7 sigma = 27; population appears to be normally distributed. 9) 99%; n = 17; a is unknown; population appears to be normally distributed. Use the given degree of confidence and sample data to construct a confidence interval for the population mean s. Assume that the population has a normal distribution. Use the confidence level and sample data to find a confidence interval for estimating the population mu. Round your answer to the same number of decimal places as the sample mean. 11) Test scores: n = 104, x = 95.3, sigma = 6.5; 99% confidence

Explanation / Answer

(8) Since we know the population standard deviation is 27, we use normal distribution.

Given a=1-0.98=0.02, the critical value is Z(0.01) = 2.33 (from standard normal table)

Answer: B

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(9)

Since the population standard deviation is unknown, we use student t distribution.

The degree of freedom =n-1=17-1=16

Given a=1-0.99=0.01, t(0.005, df=16) =2.921 (from student t table)

Answer: D

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(10) The degree of freedom =n-1=30-1=29

Given a=1-0.9=0.1, t(0.05, df=29) =1.699 (from student t table)

So the lower bound is

xbar - t*s/vn = 84.6-1.699*10.5/sqrt(30) = 81.34

So the upper bound is

xbar + t*s/vn =84.6+1.699*10.5/sqrt(30) = 87.86

Answer: B

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(11)Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So the lower bound is

xbar -Z*s/vn=95.3-2.58*6.5/sqrt(104) = 93.65557

So the upper bound is

xbar + Z*s/vn = 95.3+2.58*6.5/sqrt(104) = 96.94443

Answer: D

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