Question

A random sample size of 100 is to be taken from a population that has a proportion equal to 0.35. The sample proportion will be used to estimate the population proportion.

Calculate the probability that the sample proportion will be within ±0.05 of the population proportion.
Illustrate the situation graphically, show the calculations, and explain your results in a sentence.

Answer 1

We need to construct the 5%confidence interval for the population proportion.

The critical value for α=0.95 is zc=z1−α/2​=0.063. The corresponding confidence interval is computed as shown below:

CI =(0.35−0.063×√[0.35(1−0.35)​​/100] , 0.35+0.063×√[0.35(1−0.35)​​/100] )

CI =(0.347,0.353)​

Therefore, based on the data provided, the 5% confidence interval for the population proportion is 0.347<p<0.353, which indicates that we are 5% confident that the true population proportion p is contained by the interval

(0.347, 0.353).

Graph: