A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to...

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A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within $50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately ±$400.

a. How large a sample size is necessary?

b. If management wants to be correct to within ±$25, what sample size is necessary?

Answered Same DayDec 25, 2021

Answer To: A survey is planned to determine the mean annual family medical expenses of employees of a large...

David answered on Dec 25 2021

129 Votes

A Sample Size for 95% CI, E = 50 and σ = 400
Confidence level = 95% and Desired Margin of Error, E = 50.
Minimum sample size is given by:
P (|x̄− µ| < E) ≥ 1− α ⇒ P ( x̄− µ
σ/
√
n
< − E
σ/
√
n
) ≤ α/2
⇒ − E
σ/
√
n
≤ −zα/2 ⇒ n ≥
(
zα/2 × σ
E
)2
note: Margin of Error = (Length of CI)/2
Standard deviation: σ = 400
Significance level = α =...

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A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to...

Answer To: A survey is planned to determine the mean annual family medical expenses of employees of a large...

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