Provide an appropriate response.
-A researcher wishes to estimate the number of households with two computers. How large a sample is needed in order to be $98 \%$ confident that the sample proportion will not differ from the true proportion by more than $2 \%$ ? A previous study indicates that the proportion of households with two computers is $23 \%$.
A) 2404
B) 1701
C) 3122
D) 3

Question

Quizplus · Accepted Answer

The sample size needed can be calculated using the formula for estimating a proportion in a population: $n = \frac{{Z^2 \cdot p \cdot (1 - p)}}{{E^2}}$, where $Z$ is the Z-score corresponding to the confidence level (2.33 for 98%), $p$ is the estimated proportion (0.23), and $E$ is the margin of error (0.02). Plugging in the values: $n = \frac{{(2.33)^2 \cdot 0.23 \cdot (1 - 0.23)}}{{(0.02)^2}} \approx 2404$.

Provide an Appropriate Response 98%98 \%98% Confident That the Sample Proportion Will Not Differ from the Number

Provide an Appropriate Response $98 \%$ Confident That the Sample Proportion Will Not Differ from the Number