Question

19. In a survey of 1500 people, 945 indicated that they listened to their favorite radio station because of the music: (make sure to identify a), b), and c) correctly)

a) What is the best point estimate for the value of p?

b) Calculate the maximum error of the estimate of p with 97% confidence.

c) Construct the 97% confidence interval for the true percentage of all people who listen to their favorite radio station because of the music.

Answer 1

Solution :

Given that,

n = 945

x = 1500

a) Point estimate = sample proportion = = x / n = 945 / 1500 = 0.63

1 - = 1 - 0.63 = 0.37

b) At 97% confidence level

= 1 - 97%

=1 - 0.97 =0.03

/2 = 0.015

Z/2 = Z0.015 = 2.17

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

= 2.17 (((0.63 * 0.37) / 1500 )

= 0.027

c) A 97% confidence interval for population proportion p is ,

± E   

= 0.63 ± 0.027

= ( 0.603, 0.657 )