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The national sales manager for a textbook publishing company wishes to estimate the mean number of books sold per college. She wishes to have her estimate be within ± 30 copies and wants a 95 percent confidence interval estimate. If a pilot sample of 30 schools gave a sample standard deviation equal to 60 books, the required total sample size is less than the pilot sample already taken. True or False?

Respuesta :

Answer: It is true that required total sample size is less than the pilot sample already taken.

Step-by-step explanation:

Since we have given that

N = 30

Margin of error = E = 30

Standard deviation = 60

At 95% level of significance,

z = 1.96

So, the value of sample would be

[tex]n=(\dfrac{z.\sigma}{E})^2\\\\n=(\dfrac{1.96\times 60}{30})^2\\\\n=(1.96\times 2)^2\\\\n=3.92^2\\\\n=15.366[/tex]

So, it is true that required total sample size is less than the pilot sample already taken.

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