Question

n1=243 n2=405

pˆ1=0.72  p^2=.5  

Use this data to find the 95% confidence interval for the true difference between the population proportions.

Step 1 of 3:

Find the critical value that should be used in constructing the confidence interval

Step 2 of 3:

Find the value of the standard error. Round your answer to three decimal places

Step 3 of 3:

Construct the 95%95% confidence interval. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

= 0.72

1- = 0.28

= 0.5

1 - = 0.5

(1)

At 95% confidence level the z is ,

Z_/2 = Z _0.025 = 1.96

(2)

the value of the standard error =

[(0.72 * 0.28) / 243 + (0.5 * 0.5) / 405] = 0.038

(3)

95% confidence interval for p₁ - p₂ is ,

( - )   Z_/2  * [(1- ) / n₁ + (1 - ) / n₂]

(0.72 - 0.5)   1.96 * [(0.72 * 0.28) / 243 + (0.5 * 0.5) / 405]

0.145 < p₁ - p₂ < 0.295

(0.145 , 0.295)