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

ID: 3203782 • 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. ..... .....

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.

= 33.4, = 3.2

(a)

n = 64

x-bar = 33.4

s = 3.2

% = 90

Standard Error, SE = s/n = 3.2/64 = 0.4

Degrees of freedom = n - 1 = 64 -1 = 63

t- score = 1.669402222

Width of the confidence interval = t * SE = 1.66940222219137 * 0.4 = 0.667760889

Lower Limit of the confidence interval = x-bar - width = 33.4 - 0.667760888876548 = 32.73223911

Upper Limit of the confidence interval = x-bar + width = 33.4 + 0.667760888876548 = 34.06776089

The 90% confidence interval is [32.732, 34.068]

(b)

n = 256

x-bar = 33.4

s = 3.2

% = 90

Standard Error, SE = s/n = 3.2/256 = 0.2

Degrees of freedom = n - 1 = 256 -1 = 255

t- score = 1.650851093

Width of the confidence interval = t * SE = 1.65085109298914 * 0.2 = 0.330170219

Lower Limit of the confidence interval = x-bar - width = 33.4 - 0.330170218597827 = 33.06982978

Upper Limit of the confidence interval = x-bar + width = 33.4 + 0.330170218597827 = 33.73017022

The 90% confidence interval is [33.070, 33.730]

(c)

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

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