Question

Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 290 choosing a product at the regular price, 210 claimed to check the price before putting the item in their cart. Of an independent random sample of 210 choosing a product at a special price, 161 made this claim. Find a 95% confidence interval for the difference between the two population proportions.

Answer 1

Solution :

Given that,

n₁ = 290

x₁ = 210

₁ = x₁ / n₁ = 0.724

n₂ =210

x₂ = 161

₂ = x₂ / n₂ = 0.767

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.724 - 0.767

= -0.043

2)

Our aim is to construct 95% confidence interval.

= 1.96 (use z table)

Margin of error =   *

=  

= 0.0765

3) Required interval is

Point estimate   Margin of error

-0.172    0.037734

(-0.05 - 0.0765, -0.05+  0.0765)

(-0.119, 0.034)