Question

A manufacturer of LCD projector light bulbs is testing a new light bulb manufacturing process. They want to improve the longevity of these light bulbs they produce. However, due to the high cost associates with switching over to the new manufacturing process, they can only do so if there is clear evidence that the new production method is superior to their current production method, in terms of longer lasting LCD light bulbs

To test this, they randomly pick a sample of 85 bulbs produced using the current method, this sample yields a mean of 2850 working hours with a standard deviation of 450 hours. They also randomly choose a sample of 121 bulbs produced with the new process. This second sample yields a mean of 3100 working hours and a standard deviation of 400 hours.

a) Compute the 95% confidence interval for the average difference of the two processes then provide an appropriate conclusion here:

b) An engineer claims that the new process produces bulbs that on average last at least 500 hours longer compared to the current process. Does the confidence interval in part A support this claim? Explain why or why not.

Answer 1

a) At 95% confidence level, the critical value is z_0.025 = 1.96

The 95% confidence interval is

$(\bar x1 - \bar x2) \pm z_{0.025} * \sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}}$

$= (2850 - 3100) \pm1.96 * \sqrt{\frac{(450)^2}{85} + \frac{(400)^2}{121}}$

$=-250 \pm119.2973$

b) No, the confidence in Part A does not support the claim. Because -500 does not lie in the confidence interval.