(8 points) 3. In the workbook on page 50, we solved the following problem: A new type of light bulb was developed which is believed to last longer than ordinary light bulbs. To determine the average life of the new light bulb, a random sample of 100 light Problem continued from previous page bulbs was tested. The sample had a mean life of 1960 hours. Estimate the true mean life of the new light bulb using a 97% confidence interval. State your final conclusion using a clear, (b) As the confidence level increases, what happens to the width of the confidence interval? Use complete sentence. Assume the population standard deviation is 142 hours. clear, complete sentences to state and justify your answer. For the confidence interval, we calculated in this workbook problem, the confidence level is 97%. Using ZInterval on the calculator we found the 97% confidence interval for the mean life was 1929.2 to 1990.8 hours. Based on this sample, we are 97% confident that the mean life expectancy of all the new lightbulbs is between 1929.2 and 1990.8 hours. The length of a confidence interval is (upper bound- lower bound). For this confidence interval, the length is (1990.8-1929.2) = 61.6 hours. To find the Margin of Error, using the length of a confidence interval, we use (c) As the confidence level increases, what happens to the margin of error? Use clear, complete E = margin of error = len _ length of CI For this CI, E = 61.6 = 30.8 hours. sentences to state and justify your answer. To find the center of the CI. Center = (upper bound +lower bound) The center of this CI is Center = upper bound +lower bound _1990.8+19292 _ 3920 "20 = 1960 hours, which is the sample mean. Remember every confidence interval for the population mean is centered at the sample mean (a) Now calculate confidence intervals for the mean expectancy of all the new lightbulbs using confidence levels of 90%, 92%, 94%, 98%, and 99%. Determine the length, the margin of error and center for each CI. I have filled in the information for the 97% confidence interval we (d) As the confidence level increases, what happens to the center of the confidence interval? Use formed in the workbook. clear, complete sentences to state and justify your answer. Confidence Confidence Interval Length of CI Margin of Error | Center of CI Level 90% 93% 95% 97% 1929.2 to 1990.8 hours 61.6 hours 30.8 hours 1960 hours 98% 99% Problem is continued on the next page