Question

In a certain survey, respondents were asked if they ever hesitated to give a handshake because of a fear of germs. Of the respondents, 460 answered “yes” and 540 said “no”. (Round to three decimal place as needed) a.) What is the sample proportion of yes respondents? b.) Find 99% confidence interval for the proportion of “yes” responses.

Answer 1

Solution :

Given that Of the respondents, 460 answered “yes” and 540 said “no”

=> total respondants n = 460 + 540 = 1000

=> yes respondants x = 460

a.) => The sample proportion of yes respondents p = x/n

= 460/1000

= 0.460

b.)
=> For 99% confidence interval , Z = 2.58

=> q = 1 - p = 0.540

=> The 99% confidence interval for the proportion of “yes” responses is

=> p +/- Z*sqrt(p*q/n)

=> 0.460 +/- 2.58*sqrt(0.460*0.540/1000)

=> (0.4193 , 0.5007)

=> (0.419 , 0.501) (rounded)