Question

.NEED ANSWER ASAP

A.)

The mean and standard deviation of a random sample of n measurements are equal to 33.8 and 3.7, respectively. a. Find a 95% confidence interval for p if n = 144. b. Find a 95% confidence interval for u if n=576. 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 95% confidence interval for p if n=144 is approximately (Round to three decimal places as needed.) b. The 95% confidence interval u ifn=576 is approximately ( (Round to three decimal places as needed.) ) c. Choose the correct answer below. O A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2 O B . Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. O C . Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4 O D. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4 O E. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2

B.)

NEED ANSWERS TO A.) and B.)

Answer 1

Problem A

Answer a:

Sample size	n		144
Mean	Pbar		33.8
Confidence interval, z	95%		1.96
Standard deviation	sqrt{Pbar(1-Pbar)/n}		3.7
Margin of error	z*(STD/n)		0.0504
Upper limit	Pbar+margin		33.850
Lower limit	Pbar-margin		33.750

Answer a

for n= 144

33.750

33.850

confidence interval width= 2*margin= 0.1008

Answer b:

Sample size	n		576
Mean	Pbar		33.8
Confidence interval, z	95%		1.96
Standard deviation	sqrt{Pbar(1-Pbar)/n}		3.7
Margin of error	z*(STD/n)		0.0126
Upper limit	Pbar+margin		33.813
Lower limit	Pbar-margin		33.787

Answer b

for n= 576

33.813

33.787

confidence interval width= 2*margin= 0.0252

Answer c: D: Quadrapuling the sample size while holding the confidence level fixed decreases the width of confidence interval by a factor of 4

Ration of confidence interval width of n=144 to n=576= 0.1008/0.0252= 4

Confidence level decreased by a factor of 4

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