Question

In: Statistics and Probability

Two random samples are taken, one from among UVA students and the other from among UNC...

Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n1=81,n2=85,p^1=0.8 p^2=0.663

Find a 96.3% confidence interval for the difference p1−p2 of the population proportions.

Solutions

Expert Solution

Solution :

Given that,

n1 = 81

1 = 0.8

n2 = 85

2 = 0.663

Point estimate of difference between two proportions

= 1 -  2

= 0.8 - 0.663

=

Our aim is to construct 96.3% confidence interval.

c = 0.963

= 1- c = 1- 0.963 = 0.037

  /2 = 0.0185

= 2.086 ..(use z table)

Margin of error =   *

= 2.086 *

= 0.1692

Required interval is

Point estimate   Margin of error

0.137    0.1692

(0.137 - 0.1692 , 0.137 + 0.1692 )

(-0.0322 , 0.3062)

Required 96.3% interval is (-0.0322 , 0.3062)


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