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4. A survey of 35 individuals reveals that the proportion of people in a residential area...

4. A survey of 35 individuals reveals that the proportion of people in a residential area who patronize a particular supermarket is 0.42; a repeat of the survey in the following year, using 52 individuals finds that the proportion is 0.56. Find a 95% confidence interval for the difference in sample proportions. (3)

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Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

n1 = 35

1 = x1 / n1 = 0.42

n2 =52

2 = x2 / n2 = 0.56

1) Point estimate of difference between two proportions

= 1 -  2

= 0.42 - 0.56

= -0.14

2)

Our aim is to construct 95% confidence interval.

= 1.96 (use z table)

Margin of error =   *

=  

= 0.212

3) Required interval is

Point estimate   Margin of error

-0.14    0.212

(-0.14 - 0.212, -0.14 +  0.212)

(-0.352 , 0.072)

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