Question

The situation…

• A 12-month email study looked at the click-through responses triggered by two versions of email, Version A and Version B.

• In all 24 distributions (12 for Version A; 12, Version B) emails were drawn randomly.

• People receiving A or B versions were unrelated (randomly selected every time for both version of the email).

• The researchers had no idea which version would trigger more clicks.

• Alpha was set at p <.05.

MONTH	Group A	Group B
January	36	36
February	35	25
March	24	29
April	23	37
May	29	37
June	12	23
July	18	27
August	12	21
September	14	24
October	24	33
November	25	32
December	33	40
Mean
SD
Variance
t test
Effect Size

Answer 1

MONTH	Group A	Group B
January	36	36
February	35	25
March	24	29
April	23	37
May	29	37
June	12	23
July	18	27
August	12	21
September	14	24
October	24	33
November	25	32
December	33	40
Mean	23.75	30.33333
Standard Deviation	8.508018	6.372288

Two sample t test is used to compare the means assuming equal variance. The test is performed in following steps,

Step 1: The Null and Alternative Hypotheses

Step 2: Select the appropriate test statistic and level of significance.

The t statistic is used to compare the two population means and the significance level is for the test (Generally 5% significance level used to compare two means)

Step 3: State the decision rules.

The decision rules state the conditions that if,

,

Step 4: Compute the appropriate test statistic and make the decision.

The t statistic is used to compare the two population means. The t statistic is computed using the formula,

The P-value for the t statistic is obtained using the t distribution table for degree of freedom = n -1 = 24 -1 = 23,

Decision:

The corresponding P-value is 0.06 which is less than 0.05 at the 5% significance level for the two sided alternative hypothesis.

Step 5: State the Conclusion

The null hypothesis is rejected. Hence there is a statistically significant evidence that the Group 1 has less click-through responses ( t value is negative)

The effect size is obtained by using the formula,

Cohen's d value, d=0.2 considered a 'small' effect size, 0.5 represents a 'medium' effect sizeand 0.8 a 'large' effect size