Questions

Name _____________________________________         Statistics         Prof. Miller

Practice for Hypothesis Testing (with z)

1.    Suppose it is known that the average salary at a company is $30,000 with a standard deviation of $5,000.  You think that women get paid less than average.  Your sample of 23 women employees has a mean salary of $28,860.  Conduct a hypothesis test using a = 0.025.

2.  Light bulbs are supposed to last for 3000 hours with a standard deviation of 65 hours.  The quality control engineer samples 49 light bulbs and finds that they last for an average of 2934 hours.  Test to determine if the average life of the bulbs is significantly less than the stated life of 3000 hours using a = 0.05.

3.  A bank claims that its customers wait in line for an average of 3 minutes with a standard deviation of 1.4 minutes.  You think customers wait for more than three minutes.  You sample the waiting times of 26 customers and find a sample mean of 3.5 minutes.  Do a hypothesis test using a = 0.02.

4.  A college’s admissions guide state that students spend approximately $300 for textbooks each semester.  A random sample of 31 college students finds that the sample mean for the amount spent on textbooks is $365.  Assume that the standard deviation for the population is $75.  Test at the a = .02 level to determine if students spend significantly more than the amount stated in the admission’s guide.

5.  Suppose the mean pulse rate of college students is 68 beats per minute with a standard deviation of 12.5.  You conduct a special exercise program for 31 college students.  After completing the program, the mean pulse rate of the students was 63.1.  Test the hypothesis that the program lowered students’ pulse rates using a = 0.01.

6.  A magazine claims that its readers have an average annual income of $43,725 with a standard deviation of $3,456.  You randomly sample on 27 of the magazine’s readers and an average income of $38,251.  Determine if the income of the readers is significantly less than the income claimed by the company using a = 0.01 and the prob-value approach.