Q5. (a) The director of quality at a light bulbs factory needs to estimate the average life

of a large shipment of light bulbs. A random sample of 54 light bulbs indicated

a sample average life of 320 hours with a sample standard deviation of 81 hours. [9]

i) Construct and interpret a 95% confidence interval estimate of the true

average life of light bulbs in this shipment.

ii) Do you think the manufacturer has the right to state that the light bulbs

last an average of 370 hours? Explain.

iii) Explain why an observed value of 300 hours is not unusual, even

though it is outside the 95% confidence interval you have calculated.

(b) If we were interested in estimating the average weight of BUP male students.

How many samples should we plan on taking? We want to estimate this mean.

What do we need to consider?