Question

Gamers" are described as people who regularly play video games. A random sample of 80 people was selected and 50 were found to be male. The 95% confidence interval for the proportion based on this sample is ________. A. (0.519, 0.731) B. (0.571, 0.679) C (0.463, 0.787) D. (0.536, 0.714)

Answer 1

Solution :

Given that,

n = 80

x = 50

Point estimate = sample proportion = = x / n = 50 / 80 = 0.625

1 - = 1 - 0.625 = 0.375

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 (((0.625 * 0.375) / 80)

= 0.106

A 95% confidence interval for population proportion p is ,

± E

= 0.625 ± 0.106

= ( 0.519, 0.731 )

correct option is = A