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Chapter 8: Q.8.7 (page 456)

The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?

Short Answer

Expert verified

The required sample size is35

Step by step solution

01

Given Information

It is given that,

s =3

EBM = 1

and the confidence level is 95%

02

Explanation

If x-is used as an estimate of μ, we can be 100(1-α) % confident that the error bound EBM when the sample size is

n=(zα2σEBM)2 (1)

We know that

1. standard deviation is s= 3

2. the error bound is EBM =1

3. and the confidence level is 95%

03

The required sample size

Therefore,

α2=1−0.952=0.025⇒z0.025=1.96

Then, from Equation (1) is

n=(1.96×31)2=34.57

and because n must be an integer,the required sample size is

n=35

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