Research Question
Are the means of the median hourly wages of management occupations in the state of California higher than the that of the state of IOWA?
The research is based on a sample of 15 similar management occupations that are present in the states of California and IOWA. The research aims to establish whether the averages of the median hourly wages of these states have a statistically significant difference or not. The hypotheses for this study are:
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Null hypothesis: There is no statistically significant difference between the means of the median hourly wages of management occupation professionals in the states of California and IOWA.
Alternate hypothesis: The mean of the hourly wages of management occupations in California is larger than the mean of hourly wages of management occupations in IOWA. Therefore, there is a statistically significant difference between the 2 means.
Sample
The sample for this study has a size (n) of 15 containing the median hourly wages for workers in different management occupations. First, we assume that the sample is normally distributed. Since the sample size is smaller than 30, then we use the student’s t-test to test the hypothesis and make a conclusion.
| Management Occupations | California | IOWA |
| Chief Executives |
-$5.00 |
-$5.00 |
| General and Operations Managers |
$54.86 |
$39.30 |
| Legislators |
-$4.00 |
-$4.00 |
| Advertising and Promotions Managers |
$58.56 |
$52.52 |
| Marketing Managers |
$75.22 |
$47.21 |
| Sales Managers |
$55.78 |
$51.71 |
| Public Relations and Fundraising Managers |
$60.93 |
$43.29 |
| Administrative Services Managers |
$51.07 |
$39.30 |
| Computer and Information Systems Managers |
$80.36 |
$59.35 |
| Financial Managers |
$66.94 |
$48.21 |
| Industrial Production Managers |
$53.36 |
$44.19 |
| Purchasing Managers |
$64.47 |
$45.50 |
| Transportation, Storage, and Distribution Managers |
$46.49 |
$37.54 |
| Compensation and Benefits Managers |
$67.20 |
$45.61 |
| Human Resources Managers |
$63.60 |
$47.48 |
Calculations
Let the California group be 1 and the IOWA group be 2. Stating the hypotheses:
The level of confidence that will be used for this calculation is 95%.
From calculations in excel,
| California (1) |
IOWA (2) |
|
| Mean (X) |
52.656 |
39.4806667 |
| Stdev (S) |
24.84901343 |
18.7039413 |
| Variance (S 2 ) |
617.4734686 |
349.837421 |
| Count (n) |
15 |
15 |
Replacing the values in the formula with the ones calculated:
Then, we find the critical value at 95% confidence interval on the t-test table. To find the critical value we need to find the degrees of freedom (df).
Therefore, the critical value from the t-test table is .
Conclusion
Since the is smaller than the , we therefore fail to reject the null hypothesis that there is no statistically significant difference between the means of median hourly wages of management operations professionals. The results can be trusted this is because failing to reject the null hypothesis does not exactly mean that we have accepted the null hypothesis. It means that there is not enough evidence to reject null hypothesis.
References
California - May 2018 OES State Occupational Employment and Wage Estimates. (2019). Retrieved 11 December 2019, from https://www.bls.gov/oes/current/oes_ca.htm#00-0000
Iowa - May 2018 OES State Occupational Employment and Wage Estimates. (2019). Retrieved 11 December 2019, from https://www.bls.gov/oes/current/oes_ia.htm#13-0000
Science, B. (2019). YouTube. Retrieved 11 December 2019, from https://www.youtube.com/watch?v=pTmLQvMM-1M&t=62s
