Question

3. The general manager of Gordon's Self-Service Gasoline wants to estimate the mean number of gallons of gasoline that are purchased by customers at his Kansas City locations. He would like the estimate to be within plus or minus 0.50 gallons. Based on past studies, the standard deviation of the amount purchased is 4.0 gallons. a. How large must the sample be for him to be 99% confident about that estimate? b. How large must the sample be for him to be 95% confident about that estimate? c. How large must the sample be for him to be 90% confident about that estimate?

Answer 1

the given data are:-

population sd () = 4

margin of error (E) = 0.50

a).z critical value for 99% confidence level, both tailed test be:-

to be 99% confident about that estimate the sample size (n) must be:-

b).z critical value for 95% confidence level, both tailed test be:-

to be 95 % confident about that estimate the sample size (n) must be:-

c).z critical value for 90 % confidence level, both tailed test be:-

to be 90 % confident about that estimate the sample size (n) must be:-

we can clearly see that ,keeping everything fixed, as confidence level increases the sample size also increases.

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