Answer:
The sample should be 1,068.
Step-by-step explanation:
Consider the provided information.
Confidence level is 95% and margin of error is 0.03.
Thus,
1-α=0.95
α=0.05, E=0.03 and planning value [tex]\hat p=0.5[/tex]
Formula to calculate sample size is: [tex]n=\frac{\hat p(1-\hat p)(z_{\alpha/2})^2}{E^2}[/tex]
From the table we can find:
[tex]z_{\alpha/2}=z_{0.05/2}\\z_{0.025}=1.96[/tex]
Substitute the respective values in the above formula we get:
[tex]n=\frac{0.5(0.5)(1.96)^2}{(0.03)^2}[/tex]
[tex]n=\frac{0.25(1.96)^2}{(0.03)^2}\approx 1067.111[/tex]
Hence, the sample should be 1,068.
