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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

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Solution Summary

The confidence interval for different sample sizes have been calculated.

$2.19