Use the data in the Stem-and-leaf plot shown below listing the ages of employees in the accounting department at a company office to answer the following questions. 2 | 3 8 9
3 | 2 4 6 7 7 8
4 | 1 3 4 5 8
5 | 3 4 6
6 | 4
1. Find the mean, the standard deviation, and the 5-number summary of the data.
2. Which would be better to summarize the data, the mean and standard deviation, or the median and IQR? Why?
3. Assuming the sample is representative of a normally distributed population, find the probability of selecting an individual with an age of between 50 and 60.
4. Find the standard error of the sampling distribution, using the sample standard deviation computed in part 1 and the sample size.
5. Suppose the average age of all employees at the company is 37, and the ages of employees are normally distributed. Using the mean age of 37 and the standard error from part 4, find the probability of selecting a sample with a mean value as extreme as the mean found in part 1.
6. Use the mean and standard deviation of the sample from part 1 to construct a 95% confidence interval for the average age of employees at the company.
7. Use the mean and standard deviation of the sample from part 1 to test the hypothesis that the average age of all employees at the company is different from 37. Find the z-score and p-value.
8. Using a level of confidence of a=0.05, is there sufficient evidence to reject the null hypothesis? Interpret the conclusion in the context of the problem.
