MISS PROFESSOR ONLY

Assignment 5– Lecture 5A and Lecture 5B

Note: Show all of your steps and all working.

1. (10 points) In a simple random sample of 100 electronic components produced by a certain method, the mean lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard deviation σ =20 hours.

a. Construct a 98% confidence interval for the mean battery life.

b. Find the sample size needed so that a 99% confidence interval will have a margin of error of 3.

2. (10 points) A random sample of 45 Hollywood movies made since the year 2000 had a mean length of 111.7 minutes, with a standard deviation of 13.8 minutes. (25 points)

a. Construct a 95% confidence interval for the true mean length of all Hollywood movies made since 2000.

b. As of November 2010, three Spider-Man movies have been released, and their mean length is 120 minutes. Someone claims that the mean length of Spider-Man movies is actually less than the mean length of all Hollywood movies. Does the confidence interval contradict this claim? Explain.