The mean and standard deviation of a random sample of n measurements are equal t

ID: 3203817 • Letter: T

Question

The mean and standard deviation of a random sample of n measurements are equal to 33.4 and 3.2, respectively.

a. Find a 90% confidence interval for if n=6464. ..... , ..... (Round to three decimal places as needed.)

b. Find a 90% confidence interval for if n=256. ..... , ..... (Round to three decimal places as needed.)

c. Choose the correct answer below.

A. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.

B. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.

C. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4.

D. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

E. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.

mean 33.4 , std. deviation = 3.2

a) For 90% confidence interval z value = 1.645 , n = 64

Standard error ( SE) = std. deviation / sqrt(n)

= 3.2 / sqrt(256) = 0.2

CI = mean + / - z * SE

Lower limit = 33.4 - 1.645 * 0.2

= 33.071

Upper limit = 33.4 + 1.645 * 0.2

= 33.729

CI ( 33.071, 33.729)

b) For 90% confidence interval z value = 1.645 , n = 256

Standard error ( SE) = std. deviation / sqrt(n)

= 3.2 / sqrt(64) = 0.4

CI = mean + / - z * SE

Lower limit = 33.4 - 1.645 * 0.4

= 32.742

Upper limit = 33.4 + 1.645 * 0.4

= 34.058

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