Question

Perform t-test on eRPM for Strategy A and B. H0: A = B vs. H1: A != B (Two-sided t-test) What is the p-value?

Strategy	Date	eRPM
A	1-Jun-14	3.33
A	2-Jun-14	2.94
A	3-Jun-14	3.03
A	4-Jun-14	2.99
A	5-Jun-14	3.08
A	6-Jun-14	3.14
A	7-Jun-14	3.32
A	8-Jun-14	3.27
A	9-Jun-14	3.15
A	10-Jun-14	3.24
A	11-Jun-14	3.2
A	12-Jun-14	3.21
A	13-Jun-14	3.25
A	14-Jun-14	3.48
A	15-Jun-14	3.47
A	16-Jun-14	3.25
A	17-Jun-14	3.32
A	18-Jun-14	3.46
A	19-Jun-14	3.58
A	20-Jun-14	3.48
A	21-Jun-14	3.48
A	22-Jun-14	3.46
A	23-Jun-14	3.34
A	24-Jun-14	3.33
A	25-Jun-14	3.37
A	26-Jun-14	3.53
A	27-Jun-14	3.67
A	28-Jun-14	3.83
A	29-Jun-14	3.78
A	30-Jun-14	3.48
B	1-Jun-14	2.95
B	2-Jun-14	2.59
B	3-Jun-14	2.76
B	4-Jun-14	3
B	5-Jun-14	3.24
B	6-Jun-14	3.43
B	7-Jun-14	3.44
B	8-Jun-14	3.46
B	9-Jun-14	3.27
B	10-Jun-14	3.39
B	11-Jun-14	3.37
B	12-Jun-14	3.32
B	13-Jun-14	3.49
B	14-Jun-14	3.53
B	15-Jun-14	3.34
B	16-Jun-14	3.3
B	17-Jun-14	3.33
B	18-Jun-14	3.6
B	19-Jun-14	3.85
B	20-Jun-14	3.89
B	21-Jun-14	3.69
B	22-Jun-14	3.64
B	23-Jun-14	3.6
B	24-Jun-14	3.42
B	25-Jun-14	3.41
B	26-Jun-14	3.72
B	27-Jun-14	3.94
B	28-Jun-14	4.07
B	29-Jun-14	4.05
B	30-Jun-14	3.69

Answer 1

Answer:

For checking whether the two strategies has same eRPM or not, we have to perform hypothesis testing about the difference between two population means using t statistic (Independent samples t test).

The eRPM for strategies A and B are given as below:

eRPM for Strategy A	eRPM for Strategy B
3.33	2.95
2.94	2.59
3.03	2.76
2.99	3
3.08	3.24
3.14	3.43
3.32	3.44
3.27	3.46
3.15	3.27
3.24	3.39
3.2	3.37
3.21	3.32
3.25	3.49
3.48	3.53
3.47	3.34
3.25	3.3
3.32	3.33
3.46	3.6
3.58	3.85
3.48	3.89
3.48	3.69
3.46	3.64
3.34	3.6
3.33	3.42
3.37	3.41
3.53	3.72
3.67	3.94
3.83	4.07
3.78	4.05
3.48	3.69

For eRPM of Strategy A:

For eRPM of Strategy b:

Let us assume that, the level of significance be

Let, = Hypothesized mean eRPM for strategy A

=Hypothesized mean eRPM for strategy B

The steps for this hypothesis testing are as follows:

Step 1: Set the null and alternative hypotheses

Null hypothesis: There is no any significance difference between mean eRPM for strategies A and B (i.e., they has same eRPM (H₀: A = B)).

Alternative Hypothesis: There is significance difference between mean eRPM for strategies A and B (i.e., they do have same eRPM(H₁: A != B)).

In notation form, the hypotheses can be given as below:

Step 2: Determine the appropriate test statistic

Under the assumption of equal variance, the t formula can be stated as

can be estimated by using following formula

Step 3: Set the decision rule

Decision Rule based on critical t value:

Value of is 0.05 and the degrees of freedom is n_A+n_B-2= 30+30-2=58. The two-sided tabular t value is t_{0.05/2, 58} = t_0.025,58= 2.002. Reject the null hypothesis at 0.05 level of significance if observed t value is less than -2.002 or greater than 2.002.

Decision Rule based on p-value:

If p-value is less than or equal to the level of significance, then reject the null hypothesis and accept the alternative hypothesis.

Step 4: Computing the test statistic

From the formula for pooled standard deviation, we get

Putting this value in formula for t, we get

Test statistic, t = -0.1491

p-value = 0.1411

Step 5: Statistical Conclusion

Since, the observed t value -0.1491 is not less than the critical t value -2.002. Hence, the null hypothesis is accepted and the alternative hypothesis is rejected.

Also, p-value 0.1411 is greater than the level of significance . Hence, the null hypothesis is accepted and the alternative hypothesis is rejected.

Thus, the hypothesis testing concludes that, there is no any significance difference between the mean eRPM for strategies A and B, i.e., the strategy A and strategy B has the same eRPM.