# Sample Size

A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

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#### Solution Preview

Standard deviation =s= 0.50 pounds

confidence interval= 95%

Z corresponding to 95% and two tailed test is 1.96

We have to ensure that Z* sx < 0.20 pounds

or sx < =0.2/Z

or sx < 0.102041 =0.2/1.96

But

sx=standard error of mean=s/square root of n

s= 0.5

or n=(s^2)/(sx^2)= 25 =0.5^2/0.102041^2

sample size = 25

We will have to revise the answer as sample size is coming out to be less than 30

The sample size is coming to 25 and we are estimating the standard deviation of the ...

#### Solution Summary

Calculations have been carried out for the sample size (for estimating the population with 95% confidence).