Share
Explore BrainMass

# Confidence interval and sample size

1) Suppose that 64 smokers were sampled. Assume the sample mean and the sample standard deviation remained the same (\$20 and \$5, respectively).

a. What is the 95% confidence interval estimate of u?

b. A research a firm a conducted a survey to determine the mean amount of steady smokers spend on cigarettes during a week. A sample of 49 steady smokers revealed that X = \$20 and s= \$5. What is the 95% confidence interval estimate of u?
Explain why this confidence interval is narrower than the one determined in the previous exercise.

#### Solution Preview

1) Suppose that 64 smokers were sampled. Assume the sample mean and the sample standard deviation remained the same (\$20 and \$5, respectively).

a. What is the 95% confidence interval estimate of u?

Confidence limits

Mean=M = \$20
Standard deviation =s= \$5
sample size=n= 64
sx=standard error of mean=s/square root of n= 0.625 = ( 5 /square root of 64)
Confidence level= 95%
Therefore Significance level=alpha (a) = 5% =100% -95%
No of tails= 2
This is 2 tailed because we are calculating the 2 sided confidence interval for the average income

...

#### Solution Summary

The confidence interval for different sample sizes have been calculated.

\$2.19