In the past, the sign-up rate for your credit card has been around 6%. Your mark

Question

In the past, the sign-up rate for your credit card has been around 6%. Your marketing team wants to decide between two different sets of promotional materials that it plans to send to potential customers: a traditional set that is very similar to the one that has been used in the past, and a new, bolder set that is expected to increase the sign-up rate. Before switching to the new materials, your company wants to run a comparative experiment that evaluates the two sign-up rates. Assuming a significance level of 0.05, determine the common sample size for the two groups that can detect a 1% increase in the sign-up rate with power of 0.95. How does the sample size change if you are require less power (say, 0.90 or 0.80)? How does the sample size change if you want to detect a difference of one-half of a percent? You may want to use computer software to carry out the calculations

Explanation / Answer

Here proportion of sign - up for credit card = 0.06

Here we can detect a 1% increase

so 0.01 = margin of error = Z0.05 sqrt[p * (1-p)/ N]

0.01 = 1.96 * sqrt(0.06 * 0.94/ N)

N = 2167

so if we require less power that will decrease the critica value of Z so as sample size will also be reduced.

If we want to detect a difference of one-half of a percent

so,

0.005 = Z0.05 sqrt[p * (1-p)/ N]

0.005 = 1.96 * sqrt [0.06 * 0.94/ N]

N = 8667 (4 times the earlier N)

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