Practice for Hypothesis Testing (with z)
1. Suppose it is known that the average salary at a company is $49,029 with a standard deviation of $7,984. You think that women get paid less than average. Your sample of 23 women employees has a mean salary of $46,860. Conduct a hypothesis test using = 0.01.
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 = 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 = 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 = .02 level to determine if students spend significantly more than the amount stated in the admission’s guide.
5. A manufacturing process that has been used for many years produces light bulbs with a mean life of 1,000 hours and a standard deviation of 100. A new process has been developed. A sample of 36 tubes produced by the new process has a mean of 1,065 hours. The engineers hope that the new process produces bulbs which last longer. Do the new tubes last significantly longer? Use = .01.
6. The College Entrance Exam Board states that the mean score on the achievement test they administer is 450 with a standard deviation of 40. After tutoring a group of 100 students, you test the students and their mean is 464. Do a hypothesis test to find if the sample mean is significantly higher than the mean claimed by the CEEB. Use = .03 and the prob-value approach.