Question

Clinician at UAMS are interested in testing the effectiveness of a new recruiting method to recruit patients in a weight loss program. The recruiting method was mailed to 100 patients selected randomly from UAMS database. 50 patients responded.

1. Construct a 95% confidence interval for population proportion that respond to this new recruiting method. (8 points)

Interpret confidence interval in part a in the context of this question. (2 points)

Answer 1

Solution :

Given that,

n = 100

x = 50

Point estimate = sample proportion = = x / n = 50 / 100 = 0.500

1 - = 1 - 0.500 = 0.500

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 ((( 0.500 * 0.500) / 100 )

= 0.098

At 95% confidence interval for population proportion p is ,

- E < p < + E

0.500 - 0.098 < p < 0.500 + 0.098

0.402 < p < 0.598

( 0.402 , 0.598 )

The 95% confidence interval for the true population proportion p is : ( 0.402 , 0.598 )