Question

The sample size needed to estimate a population mean to within
50 units was found to be 97. If the population standard deviation
was 250, then the confidence level used was:

a) 90%

b) 95%

c) 98%

d) 99%

e) None of the above.

Answer #1

Solution :

Given that,

standard deviation = = 250

margin of error = E = 50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} =
Z_{0.025} = 1.96

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

= ((1.96 * 250) / 50)^{2}

= 97

Sample size = 97

Confidence level = 95%

Option b) is correct .

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