Question

In: Statistics and Probability

There is no information at all about the possible proportion of cat lovers in a large...

There is no information at all about the possible proportion of cat lovers in a large population. There's also no time to run a trial poll. A researcher wants to build a 95% confidence interval for the population proportion with the margin of error 3%. The number of the valid answers that the researcher must obtain is

Expert Solution

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.03)2 * 0.5* 0.5

= 1067.11

Sample size =1067

orchestra answered 2 years ago

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