1. The labor relations manager of a large corporation wished to study the absenteeism among workers at the company's central office during the last year. A random sample of 25 workers revealed the following: an average of 9.7 days; a standard deviation of 4.0 days; and 12 employees were absent more than 10 days. Set up a 95% confidence interval estimate of the average number of days absent for the company's workers last year.
2. The labor relations manager of a large corporation wished to study the absenteeism among workers at the company's central office during the last year. A random sample of 25 workers revealed the following: an average of 9.7 days; a standard deviation of 4.0 days; and 12 employees were absent more than 10 days. Set up a 95% confidence interval estimate of the proportion of workers absent more than 10 days last year.
3. You are considering investing in a company. The company claims for the past few years the average monthly return on such an investment has been $870 with a standard deviation of $50. You sample 30 investors and determine the sample average return to be $855. Using a .05 level of significance would you conclude that the true average return is different from $870? Explain your conclusión.
4. A random sample of 400 college students was selected and 120 of them had at least one motor vehicle accident in the previous two years. A random sample of 600 young adults not enrolled in college was selected and 150 of them had at least one motor vehicle accident in the previous two years. At the .05 level, is there a significant difference in the proportions of college students and similar aged non college students having accidents during the two year period? Explain your conclusion.
5. A statewide real estate company specializes in selling farm property in the state of Nebraska. Their records indicate that the mean selling time of farm property is 90 days. Because of recent drought conditions, they believe that the mean selling time is now greater than 90 days. A statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. At the .10 significance level, has there been an increase in selling time?
6. The policy of the Suburban Transit authority is to add a bus route if more than 55 percent of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 42 would use a proposed route from Bowman Park to the downtown area. Does the Bowman-to-downtown route meet the STA criterion? Use the .05 significance level.
7. An industrial engineer at Lyons Products would like to determine whether there are more units produced on the afternoon shift than on the morning shift. A sample of 50 morning-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the mean number of units produced on the afternoon-shift larger?
8. The manager of a package courier service believes that packages shipped at the end of the month are heavier than those shipped early in the month. As an experiment, he weighed a random sample of 20 packages at the beginning of the month. He found that the mean weight was 20.25 pounds and the standard deviation was 5.84 pounds. Ten packages randomly selected at the end of the month had a mean weight of 24.80 pounds and a standard deviation of 5.67 pounds. At the .05 significance level, can we conclude that the packages shipped at the end of the month weigh more?
9. A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. Is there evidence of an improvement on the final?
10. There are two car dealerships in a particular area. The mean monthly sales at the two dealerships are about the same. However, one of the dealerships (dealership A) is boasting to corporate headquarters that his dealership's monthly sales are more consistent. An industry analyst reviews the last seven months at dealership A and finds the standard deviation of the seven monthly sales to be 14.79. He reviews the last eight months at dealership B and finds the standard deviation of the eight monthly sales to be 22.95. Using the .01 significance level does the analyst find evidence that the boast of dealership A is correct?