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

Question

The mean and standard deviation of a random sample of n measurements are equal to 33.4 and 3.9, respectively. a. Find a 90% confidence interval for mu if n = 100. b. Find a 90% confidence interval for mu if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 90% confidence interval for mu if n = 100 is approximately (Round to three decimal places as needed.)

Explanation / Answer

a) The statistical software output for this is:

One sample T confidence interval:
: Mean of population

90% confidence interval results:

Hence,

90% confidence interval is:

(32.752, 34.048)

b) The statistical software output for this is:

One sample T confidence interval:
: Mean of population

90% confidence interval results:

Hence,

90% confidence interval is:

(33.079, 33.721)

c) The width becomes half of the original width.

Mean Sample Mean Std. Err. DF L. Limit U. Limit 33.4 0.39 99 32.752447 34.047553

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