Question

Bright Bulb light bulb company is planning a study to assess the average life expectancy of their light bulbs. They know the standard deviation is σ = 400 hours. They want a 95% confidence interval with a margin of error of 50 hours. What sample size do they need?

Answer 1

Answer:

Sample size = 246 .

Step-by-step explanation:

We are given that Bright Bulb light bulb company is planning a study to assess the average life expectancy of their light bulbs. For this they know;

Standard deviation, $\sigma$ = 400 hours         Confidence interval = 95%

Margin of error = 50 hours

We know that Margin of error formula is given by;

    Margin of Error = $Z_\frac{\alpha}{2} * \frac{\sigma}{\sqrt{n} }$   where $\alpha$ = 5%

                   50       =  1.96 * $\frac{400}{\sqrt{n} }$  

                     $\sqrt{n}$  =  $\frac{1.96*400}{50}$ = 15.68

                      n  =  $15.68 ^{2}$ = 245.86 ≈ 246

So, sample size needed will be 246 bulbs.