Question

Two proposed advertising campaigns themes for a new product are being evaluated for effectiveness. A random sample of 120 consumers is exposed to theme A, and another sample of 100 consumers is exposed to theme B. The study asks each customer whether they have a positive opinion of the product.

• 78% of the theme A participants said, yes, they have a positive opinion about the product.
• 64% of the theme B participants said, yes, they have a positive opinion about the product.

Is there enough evidence to support the claim that theme A is a more effective campaign than theme B, with an a = 5% level of significance?

Answer 1

Let

We are testing :

We know that :

Now, we are given that :

Thus, the value of the test statistic :

Now, the test here is right tailed, thus the critical region lies in the right tail.

We find the 5% point (from the right) of the standard normal distribution and we get:

z_0.05 = 1.644854

Since, the value of the test statistic is greater than the critical point, we reject H₀ : p_A = p_B and conclude that there is enough evidence to support the claim that theme A is more effective campaign than theme B at 5% level of significance.

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