Mis171 Business Analytics | Cleveland Assessment Answers

1.An estimate of:

1. the mean salary for ALL Cleveland employees.
2. the proportion of ALL Cleveland employees who are very satisfied and moderately satisfied with their job.

2.The mean salary across the industry is $28,500. Senior management claims that our employees earn more than the industry average. Check the validity of this claim?

3.Senior management also believes that the proportion of employees who moderately satisfied and very satisfied with their job is at least 92%. Is this true?

4.Is there a significant difference in the mean salary of ALL male and ALL female employees?

 a.the mean salary for ALL Cleveland employees to within $900, with 95% confidence?

 b.the proportion of ALL Cleveland employees who are very satisfied and moderately satisfied with their job to within 2%, with 95% confidence?

Answers:

Mean Salary For Cleveland Employees

The mean salary for Cleveland employees can be obtained by running a descriptive statistics for salary. This is because mean is one of the measures of central tendencies contained as an item in the summary statistics.

The table below shows the summary statistics for employees’ salary

Table 1

The mean salary can be extracted from the summary table above. The mean salary for Cleveland employees is 29.49 thousand dollars (29490 dollars).

Proportion Of Very Satisfied And Moderately Satisfied Employees

The table of number of workers and their rates of satisfaction

Table 2

It can be observed that those who are very satisfied constitutes to 45.66% while those who are moderately satisfied constitutes to 43.43%.  Therefore the moderately and the very satisfied are 89.04% of the total employee population.

3.0 Test That The Mean Salary Is 28,500 Dollars (28.5 Thousand Dollars)

Prior to establishing the test results, a hypothesis must be put forward. A one sample t-test is employed in this test to establish whether the mean salary of employees at Cleveland is above 28,500 dollars.

Hypothesis

H₀: Mean salary of Cleveland employees is more than 28,500 dollars

Versus

H₁: Mean salary of Cleveland employees is not more than 28,500 dollars

The test has been carried out at 95% confidence level

The results of the analysis of variance are as in the table below

Table 3

Since the p-value is greater than .05 we fail to reject the null hypothesis. We therefore conclude that the mean salary of Cleveland employees is more than 28,500 dollars.

Proportion Of Employees At Least 92%?

Table of distribution of employees according to their satisfaction

Table 4

It can be observed that those who are very satisfied constitutes to 45.66% while those who are moderately satisfied constitutes to 43.43%.  Therefore the moderately and the very satisfied are 89.04% of the total employee population. So the claim that the proportion of very satisfied and moderately satisfied employees is at least 89.04% is not true.

Test For Significant Difference In Salary Between Men And Women

Since there are two variables only which form a pair, a t-test is appropriate for this kind of test. The research survey sought to establish whether there was a significant difference in the salaries of male and salary of females. The research came up with a hypothesis to guide the test as follows;

H₀: There is no significant difference between the salaries for the male and female workers in Cleveland

Versus

H₁: There is a significant difference between the salaries for the male and female workers in Cleveland

Level of significance is 0.05

Table 5

It can be observed from the result table above that the p-value is .00. This is less compared to the level of significance which is .05. The null hypothesis is therefore rejected and the alternative accepted (Woodward, 2007) . In conclusion, it can therefore be said that there is a significant difference in amount of salary between male and female.

Confidence Intervals

1. a) Confidence interval for mean =

Mean = 28500 n = ?

1. b) 2% of 9000

A sample size of 180 will be appropriate