Answer to Question #123302 in Statistics and Probability for Oduro

Question

A research was conducted to estimate the proportion of ARB Bank customers who could recognize the existing Government Treasury Bill investment product and the flagship investment product of the bank. Out of a sample of 3000 customers, 1200 were able to recognize the existence of the Government Treasury Bill, whilst 800 out of the 3000 sample were also able to recognize the existence of the bank’s flagship investment product.
Using 95% degrees of confidence,
Construct the confidence interval for the difference between two population proportions.
Construct the confidence interval for the difference between two population percentages.

Answer 1

n₁=3000

x₁=1200

n₂=3000

x₂=800

Confidence level=95%

The sample proportions can be obtained as:

p₁=x₁/n₁=1200/3000=0.4

p₂=x₂/n₂=800/3000=0.267

The critical value of Z at 95% confidence level from the standard normal table is 1.96.

The required 95% confidence interval can be obtained as:

CI=(p₁-p₂)±Z_a/2$\sqrt{p1(1-p1)/n1+p2(1-p2)/n2}=(0.4-0.267)±(1.96)\sqrt{0.4*(1-0.4)/3000+0.267*(1-0.267)/3000}=0.113±-0.0236=(0.1094,0.1566)$

percentage- 10.94%-15.66%