The accuracy of a labour standard is to be within 5%, and the confidence level is 95%. The standard deviation of the sample is 2 and the mean is 8. What sample size should be used?
A) 8
B) 10
C) 96
D) 127
E) cannot be determined from the information given

Question

Quizplus · Accepted Answer

To determine the sample size needed for a specific accuracy and confidence level, you can use the formula for the sample size in estimating a mean with a specific confidence level and margin of error (E):$$ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 $$Where:- $ n $ is the sample size,- $ Z $ is the Z-score corresponding to the desired confidence level (for 95%, $ Z = 1.96 $),- $ \sigma $ is the standard deviation of the population (given as 2),- $ E $ is the desired margin of error (for 5% accuracy on a mean of 8, $ E = 0.05 \times 8 = 0.4 $).Plugging in the values:$$ n = \left( \frac{1.96 \times 2}{0.4} \right)^2 $$$$ n = \left( \frac{3.92}{0.4} \right)^2 $$$$ n = \left( 9.8 \right)^2 $$$$ n = 96.04 $$Since the sample size must be a whole number, and you can't have a fraction of an observation, you round up to the nearest whole number, which gives you 96.

The Accuracy of a Labour Standard Is to Be Within