Question

Please help me.

A random sample of 16 light bulbs has a mean life of 650 hours and a standard deviation of 32 hours. Assume the population has a normal distribution. Construct a 95% confidence interval for the population mean.

Answer 1

Step-by-step Answer:

Mean = mu = 650

Standard deviation = sigma = 32

Sample size = 16

Therefore standard error of the given sample

standard error

=  standard deviation / sqrt(N)

= standard deviation /sqrt(16)

= 32/4

= 8

For 95% confidence interval, we need the normal curve to have an area of 0.95 between the limits, which, from normal distribution tables, the Z-value of 97.5% is 1.96, which means that for a 95% confidence interval, the values are between +/- 1.96 standard deviations, or +/- 1.96*8= +/- 15.68 hours.

Thus the confidence interval is

650 - 15.68 hours < X < 650+15.68 hours

634.32 < X < 665.68 hours