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Explanation & Answer
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. Sample Design
Based on the data that was provided from Kafalah, the treatment group included 3,390
respondents, and the control group was 611 respondents. The margin of error was considered as
5% (0.05). The respondents in treatment groups were distributed by month. The appropriate
sampling with respondents proportionally distributed in the month was obtained. For this, the
proportion of treatment and control group in all observations was calculated as follows:
For the control group:
p = Control group / Total = 3,390 / 4,001 = 0.8473
The proportion of the control group:
q = 1 − p = 1 − 0.8473 = 0.1527
Then, the proportional sampling was calculated using the formula for sample size based on
proportions. The sample size n was obtained as:
𝑛=
1.952 𝑝̅ (1 − 𝑝̅ )
0.052
where 1.95 is Z value for a 95% confidence interval based on normal distribution, and 0.05 is the
desired margin of error. The proportional sampling result is 196.8. The clustering effect is
considered here by multiplying the proportional sampling result by a factor of 1.2:
196.8 × 1.2 = 236.16
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