Question

The mean and standard deviation of a random sample of n measurements are equal to 34.7 and 3.6, respectively a. Find a 99% confidence interval for μ if n: 49. b. Find a 99% confidence interval for μ if n-196. 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 99% confidence interval for if n-49 is approximately (Round to three decimal places as needed.) ( ) b. The 99% confidence interval if n 196 is approximately Round to three decimal places as needed.) c. Choose the correct answer below A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2. B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4 ° C. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. O D. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. E. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2

Answer 1

Solution:- Given that mean = 34.7, standard deviation = 3.6

99% confidence interval for Z = 2.576

a. 99% confidence interval for μ = X +/- Z*σ/sqrt(n)

= 34.7 +/- 2.576*(3.6/sqrt(49))

= 33.375 , 36.025

b. 99% confidence interval for μ = X +/- Z*σ/sqrt(n)

= 34.7 +/- 2.576*(3.6/sqrt(196))

= 34.038 , 35.362

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