Question

A testing engineer in a light bulb factory is planning a study to estimate the average life of a large shipment of light bulbs. The engineer wants to estimate the average life within plus or minus 16 hours with 95 percent confidence. Assuming a process standard deviation of 90 hours, determine the sample size for this study.
a. 7
b. 43
c. 58
d. 122

Answer 1

Answer: d. 122

Step-by-step explanation:

Formula to find sample size : $n=\left ( \dfrac{\sigma\times z}{E} \right )^2$ , where $\isigma$ = prior population standard deviation, z= Critical z-value for confidence level and E = Margin of error.

As per given ,

$\sigma=90\ hours\\\\E=\pm16\ hours$

Also , for 95% confidence level , z-value = 1.96

Now , Required sample size would be

 $n=\left ( \dfrac{90\times1.96}{16} \right )^2\\\\=\left(11.025\right)^2\\\\=121.550625\approx122$

Hence, the required sample size =122

Thus , the correct option is d. 122.