Reference no: EM132580765
1. A tire manufacturing company is reviewing its warranty for their rainmaker tire. The warranty is for 40,000 miles. The distribution of tire wear is normally distributed with a population standard deviation of 15,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A sample of 49 tires revealed that the mean number of miles is 45,000 miles. Test the hypothesis with a 0.05 significance level. What is our decision?
2. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To determine if the spark plugs average 22,100 miles, what is the critical value for the test using a 0.05 level of significance?
3. A machine cuts steel to length for nails. The mean length of a nail is 43 millimeters. There is concern that the settings of the machine producing the nails have changed. To test the claim, 12 nails (n = 12) were sampled. The mean of the sample is 41.5 and the standard deviation 1.784. To decide if the sample data support the claim that the mean length is 43 millimeters, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
4. A committee that is studying employer-employee relations proposed that each employee would rate his or her immediate supervisor, and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal. We test the hypothesis that the population proportions are equal with a 0.05 significance level. What is our decision?
5. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience was $1,875. Using the 0.05 significance level, what is the decision regarding the null hypothesis?