When 415 college students are randomly selected and surveyed, it is found that 328 made online purchases during the last month.

When 415 college students are randomly selected and surveyed, it is found that 328 made online purchases during the last month. What sample size will produce a margin of error of 6% with 95% confidence level?

Expert Solution

Number of Items of Interest,   x =   328
Sample Size,   n =    415

Sample Proportion ,    p̂ = x/n =    0.7904

--------------------------

sample proportion ,   p̂ =    0.7904
sampling error ,    E =   0.06
Confidence Level ,   CL=   0.95

alpha =   1-CL =   0.05
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]

Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (   1.960   /   0.06   ) ² *   0.79   * ( 1 -   0.79   ) =    176.8


so,Sample Size required=       177

orchestra answered 3 years ago

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