Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college​ campuses, you believe the proportion will be near 30​%. What sample size is needed if you wish to be 98​% confident that your estimate is within 0.02 of the true​ proportion?

Answer 1

Solution :

Given that,

= 30% = 0.30

1 - = 1 - 0.30 = 0.70

margin of error = E = 0.02

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z/2 = Z0.01 = 2.326

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.326 / 0.02)2 * 0.30 * 0.70

= 2840.3649 = 2841

Sample size = 2841

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