Question

You are concerned that you did not sample the correct number of 5-year-olds. You know that the standard deviation of all 5-year-old females' heights is 0.75 inches. You want to be 99% confident that the mean is correct within 0.25 inches.

How many 5-year-old females should you sample?

Is a sample of 80 large enough? Yes No

Answer #1

Solution :

Given that,

= 0.75

E = 0.25

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_{/2}
= Z_{0.005} = 2.576

sample size = n = (Z_{/2}*
/E)2

= (2.576 * 0.75 / 0.25 )2

n= 59.72

n= 60

The following data represents the height in inches of 80
randomly selected 5 year-olds.
44.5,45.4,39.6,45.5,42.0,44.5,39.5,42.3,44.0,37.7,42.4,43.0,44.7,43.3,42.2,37.6,43.6,44.6,35.9,34.6,42.2,43.4,63.5,41.2,38.5,42.2,41.3,40.5,43.7,42.4,46.2,44.7,42.7,40.5,43.6,40.3,38.8,37.4,48.1,42.7,45.7,38.6,40.6,44.4,40.6,48.5,41.9,44.5,38.7,47.0,44.8,41.6,47.5,42.6,45.0,41.6,40.3,40.7,46.0,42.8,43.3,50.2,48.4,42.0,40.7,41.7,42.1,38.2,43.4,39.9,39.5,46.9,37.5,40.3,36.3,38.9,41.9,42.6,44.6,42.3
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