How to find sample size using range rule of thumb

Asked by admin @ in Mathematics viewed by 294 People

A student wants to estimate the mean score of all college students for a particular exam. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible scores range from 300 to 2200. Use technology and the estimated standard deviation to determine the sample size corresponding to a 90​% confidence level and a margin of error of 100 points. What​ isn't quite right with this​ exercise? The range. rule of thumb.estimate for the standard deviation. nothing.

Answered by admin @


Answer:

See explanation below

Step-by-step explanation:

range = 2200 - 300 = 1900

To find standard deviation, we have:

standard deviation = range/4 = \frac{1900}{4} = 475

The range rule of thumb estimate for the standard deviation is 475

Given:

Standard deviation, \sigma = 475

Margin of Error, ME = 100

\alpha = 1 - 0.90 = 0.10

Za/2 = Z0.05 = 1.64

Find sample size, n:

n ≥ [Z_\alpha_/_2 * (\frac{\sigma}{ME})]^2

n ≥ [1.64 * (\frac{475}{100})]^2

n ≥ 60.68

≈ 61

Minimun sample size,n = 61


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