4. Sample size for an interval estimate of a population mean Aa Aa The Illinois

Question

4. Sample size for an interval estimate of a population mean Aa Aa The Illinois State Toll Highway Authority is conducting a study to estimate the mean one-way distance to work for likely toll-road commuters. The study researcher desires a 2-mile margin of error at 95% confidence. The population standard deviation is unknown, so a best guess is used as the planning value for . The highway authority estimates that the smallest distance to work in the population of low-income consumers is 3 miles, and the largest distance to work is 90 miles A rough approximation of the population standard deviation is 90 43.5 87 Use the Distributions tool to help to answer the question that Select a Distribution Distributions To satisfy the requirement for the margin of error, a sample size no smaller than is needed.

Explanation / Answer

Thumb rule for relation between range and standard deviation is :

standard deviation *4 = range

Standard deviation = (range)/4 = (max-min)/4 = 90-3 / 4 = 87/4 = 21.75

Now, to solve for minimum sample size:

Margin of error = Z*sigma/sqrt(n), values of Z is 1.96 @ 95% CI, MOE = 2 as given and sigma taken out above is 21.75. Subbing,

2 = 1.96*21.75/sqrt(n)

n = (21.75*1.96/2)^2 = 454.33

So, 455 is the right answer.

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