Question

Once you have the dataset, please use knowledge gained in other business and/or economics classes to realize what topic and theory the data could relate and a research question that it could allow you to answer. More specifically, please put together an analysis by making sure your project report includes the following:

1. Brief statement of the research topic and problem. As you get the dataset from me, you would need to use some imagination what research problem that data could be related to. Nevertheless, please state very briefly (i.e. in one paragraph) what theory (research literature or textbooks related to business or economics) says about the research problem – e.g. is there some dilemma or controversy that your research will help to clarify.
2. Clearly worded research question that limits the research problem to researchable task. (This is a short sentence that ends with the question mark and it is suggested that you draw from theory (research literature / textbook knowledge) in one of the business studies field to word it!)
3. Please identify the type of data that you are working with – on what type of measurement scale(s) where the selected variables measured by the original data collectors. (As you work with the dataset given by me, use your educated guess).
4. Describe the data with the tools of descriptive statistics, using both numerical as well as graphical methods. In addition to reporting and commenting on the values central tendency and diagrams, please also justify the choice of method (e.g. why a particular kind of measure of central tendency was selected and the chosen graphic is appropriate to use in this context).
5. Justify the selection of the specific data analysis method of inferential statistics. Recommendation – use the decision tree (introduced in Ch. 9ff) to make the selection and justification of it. You should look up also the assumptions and comment how your data meets them but I will not penalize you if it does not meet all the criteria. Nevertheless, please make sure that you include the basic information about distribution of the variables – are they more or less normally distributed (use both numerical as well as graphical methods). It is required that you restrict the choice of data analysis method(s) to the ones introduced in the class. (In addition to the fact that we covered only the most basic / frequently used methods in class, also the spreadsheet program (Excel) which the textbook is based on and that I presented during the course, has limited set of methods available).
6. Formulate the null and research (alternative) hypothesis – similarly to point 2 it is recommended that you word them on the basis of research literature / textbook knowledge in one of the business studies field that you know);
7. Determine the test criteria:

7.1. Specify the level of significance (Type I error associated with the null hypothesis),

7.2. Determine the test statistic (the appropriate statistical test as mentioned under point 5 above),

7.3. Determine the critical values (and region(s) if applicable),

8. Calculate the value of the test statistic (obtained value).
9. Make a decision about the null and research hypothesis by comparing the obtained value to the critical value and interpret the results of the data. You can pay attention also to the p-values.
10. Sum up you research report by relating the statistical test result(s) to the research question and theory that you set to test.

ID	Nr. of units produced before new compensation system	Nr. of units produced after new compensation system
1	20	23
2	6	8
3	12	11
4	34	35
5	55	57
6	43	76
7	54	54
8	24	26
9	33	35
10	21	26
11	34	29
12	33	31
13	54	56
14	23	22
15	33	35
16	44	41
17	65	56
18	43	34
19	53	51
20	22	21
21	34	31
22	32	33
23	44	38
24	17	15
25	28	27
26	47	50
27	35	78
28	29	29
29	36	44
30	25	23

Answer 1

Research question:

Does new compensation system affect the number of units produced?

Hypothesis:

That is new compensation system does not affect the number of units produced.

Que.7.1

Level of significance : It is the probability of rejecting null hypothesis when it is true.

Here we assume it is 5%.

Que.7.2

Test statistics:

Here we use paired t test.

Where

I used R software to solve this question.

R codes and output:

before=scan('clipboard');before
Read 30 items
[1] 20 6 12 34 55 43 54 24 33 21 34 33 54 23 33 44 65 43 53 22 34 32 44 17 28
[26] 47 35 29 36 25
> after=scan('clipboard');after
Read 30 items
[1] 23 8 11 35 57 76 54 26 35 26 29 31 56 22 35 41 56 34 51 21 31 33 38 15 27
[26] 50 78 29 44 23
> t.test(before,after,paired=TRUE)

Paired t-test

data: before and after
t = -1.0769, df = 29, p-value = 0.2904
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-5.991486 1.858153
sample estimates:
mean of the differences
-2.066667

Test statistic = t = -1.0769

DF = 29

Hence from t table critical value at 5% level of significance is 2.045

P-value = 0.2904

Since p-value is greater than 0.05, hence we accept null hypothesis and conclude that new compensation system does not affect the number of units produced.