Question

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is 1.6? The population standard deviation is known to be 10.36.

*a) n* = 102

*b) n* = 103

*c) n* = 161

*d) n* = 162

Answer #1

Given that,

standard deviation = = 10.36

margin of error = E = 1.6

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 =1.96

Sample size = n = [(Z/2 * ) / E]2

= ((1.96 *10.36) /1.6)2

= 161.06

**Sample size = 162**

**Correct option = d) n = 162**

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