Engineering Probability and Inference Homework 2 1

Engineering Probability and Inference Homework 2

1.    Independent samples of two lighting techniques are compared to measure the intensity of light at selected locations. If 61 measurements in the first area had an average output of 55 foot-candles with a standard deviation of 2.7 foot-candles and 41 measurements in the second area had an average output of 60 foot-candles with a standard deviation of 4.2 foot-candles. Find a 95% confidence interval estimate for the variance of the second area.

2.    Using the information in Problem #1, use a 5% significance level to test if there is a difference between the two variances.

3. The Federal Reserve System reports that out of 260 Americans under 35 years old surveyed, 44 of them owned stocks. Out of 250 Americans between 35 and 44 surveyed, 56 owned stock. Find a 98% confidence interval for the difference between the proportion of Americans under 35 who own stock and the proportion of Americans between 35 and 44 who own stock? Round to 3 decimal places. Based on your interval, do you think there is a difference in the proportion of under 35s who own stock and the proportion of 35-44 year olds who own stock? WHY?

4. In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane. Find a 92% confidence interval estimate for the true proportion of cars that pull into the correct lane when making a right turn.

5. A drone manufacturer claims that more than 90% of their drones can pass an initial test to fly for 2 hours before needing to be recharged. A group selected 85 claims and found that 78 of them were able to pass the initial test. Using α=0.05, test the claim that more than 90% of the drones pass the initial test.                          

6. If 46 of 400 tires of Brand A failed to last 30,000 miles, while 62 tires out of 400 for Brand B failed to last 30,000 miles. Use α=0.05 to test the claim that there is no difference in the durability of the two kinds of tires.

7. The following data refer to repairs made on motors for three different shops. When a motor is returned to a testing center, it is labeled as complete, requiring an adjustment, or an incomplete repair. Use a 0.05 significance level to test whether the three shops have homogeneous repairs.

8. The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of work among the three daily shifts. She randomly selects tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. Use the following data and α=0.01 to test if quality of work and shift are independent.