Good Current Production Method: The Number Of Produced Units Using Current Method Of Production Essay Example

Inferential Statistics and Findings

In this paper I will show the basics of statistics and probability theory application to a real-world problem. My goal is to check whether current production of a company is significantly different from proposed production. I will use statistical testing to check this claim.

I’m given with the data of 30 observations (30 hours recorded) of two variables:

Proposed production method: the number of produced units using proposed method of production.
I begin with descriptive statistics for these variables:

Descriptive Statistics: Current Production Method; Proposed Production Method

Variable N N* Mean SE Mean StDev Minimum Q1 Median
Current Production Metho 30 0 50478 391 2144 46200 49093 52015
Proposed Production Meth 30 0 53143 4,63 25,4 53125 53125 53133
Variable Q3 Maximum
Current Production Metho 52080 52083
Proposed Production Meth 53151 53204
Now I test the claim using two-sample Student’s t-test for independent samples:
H0: μ1=μ2Ha: μ1≠μ2

Set level of significance alpha:

a=0.05

Perform testing:

Two-Sample T-Test and CI: Current Production Method; Proposed Production Method
Two-sample T for Current Production Method vs Proposed Production Method
N Mean StDev SE Mean
Current Production Metho 30 50478 2144 391
Proposed Production Meth 30 53143,0 25,4 4,6
Difference = mu (Current Production Method) - mu (Proposed Production Method)

Estimate for difference: -2665

95% CI for difference: (-3466; -1865)
T-Test of difference = 0 (vs not =): T-Value = -6,81 P-Value = 0,000 DF = 29
Since p-value of the test is less than 0.001, I reject the null hypothesis. There is enough evidence to say that the production level is significantly different between current method and proposed method (at 5% level of significance).
The 95% CI for difference (highlighted with yellow) shows that I’m 95% confident that the difference between population averages is between 3455 and 1865 units.

References

Casella, G., & Berger, R. (2002). Statistical inference (2nd ed.). Australia: Thomson Learning.