CALCULATE ALL THE FOLLOWING AND INTERPRET RESULTS

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The population standard deviation of light bulb production process is known to be 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours. (a) Write down the parameter of interest, its point estimator and the associated sampling distribution which could be used for the estimation of the confidence interval. Provide a brief explanation. (Marks: 3) (b) Specify the formula for 90% confidence interval estimator of the parameter. (Marks: 1) (c) Perform the necessary calculations and write down the lower and upper limits of the 90% confidence interval. (Marks: 3) (d) Interpret the confidence interval. (Marks: 1) (e) Do you think that the manufacturer has the right to state that the light bulbs produced in his factory last an average life of 400 hours? Explain. (Marks: 2)