Question 1

A tire company performs quality-control tests on the monthly output of its best-selling model tire at each of its plants. Each month a random sample of 25 tires is selected from each plant and tested to see if the average tread life of that plant's tires is above specifications. For one plant, the random sample of 25 tires had a sample mean of 39,500 miles and a sample standard deviation of 3,300 miles. The company performs a hypothesis test at the .05 level of significance to see if there is evidence that the average tread life is greater than 38,000. Based on this sample, the company should:

Fail to reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles.

Reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Fail to reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles

Question 2

Consider the following set of numbers: 10, 25, 13, 18, 40, 5. Determine the median and variance of these data.

median = 15.5, variance = 157.9

median = 15.5, variance = 35

median = 18.5, variance = 473.83

median = 18.5, variance = 12.57

Question 3

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Calculate the test statistic for the sample data.

Question 4

Consider the following data on the number of beers consumed by a sample of football fans during a game:

Calculate the variance.

Question 5

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the margin of error (in hours) for the 90% confidence interval for this sample.

Question 6

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the lower confidence limit (LCL), in hours, for the 90% confidence interval for this sample.

Question 7

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the upper confidence limit (UCL), in hours, for the 90% confidence interval for this sample.

Question 8

A tire manufacturer selected a random sample of 50 tires of a particular model chosen from the past month's production and used destructive testing to determine the tread life of each tire. The sample mean was 42,300 miles and the sample standard deviation was 7,500 miles. What is the 95% confidence interval estimate for the tread life of that entire model produced in the past month?

Question 9

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution. What is the probability of four or more complaints during the next four weeks?

Question 10

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of exactly three complaints during the next two weeks?

Question 11

Zombies eat, on average, 5 brains per day. Assume the actual number of brains eaten per day follows the normal distribution with a standard deviation of 0.29 brains. What is the probability that a zombie will eat exactly 3.2 brains tomorrow?