Question

A quality 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 15 hours with 95 percent confidence. Assuming a process standard deviation of 100 hours, determine the sample size for this study

Answer 1

Answer:

The required sample size is 171.

Step-by-step explanation:

Consider the provided information.

The engineer wants to estimate the average life within plus or minus 15 hours with 95 percent confidence. Assuming a process standard deviation of 100 hours,

First calculate the value of $Z_{\frac{\alpha}{2}}$

By using the table we get.

$Z_{\frac{\alpha}{2}}=1.96$

Now use the formula: $N=(\frac{Z_{\frac{\alpha}{2}}\times \sigma}{E})^2$

Substitute the respective values in the above formula we get.

$N=(\frac{1.96\times 100}{15})^2$

$N=(\frac{1.96\times 100}{15})^2$

$N=(\frac{196}{15})^2=170.73777$

$N\approx171$

Hence, the required sample size is 171.