Answer: a) [tex](79.8\%,\ 97.1\%)[/tex]
b) 8.2%
Step-by-step explanation:
Given : Sample size : [tex]n=60 [/tex]
Number of students will be going to college= 53
The proportion of students will be going to college: [tex]p=\dfrac{53}{60}\approx0.88[/tex]
Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Margin of error : [tex]E=z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]E=(1.96)\sqrt{\dfrac{(0.88)(1-0.88)}{60}}\\\\\ E=0.0822266136965=0.082\approx8.2\%[/tex]
The confidence interval for population proportion is given by :-
[tex]p\pm E\\\\\approx(0.88-0.082,0.88+0.082)=(0.798,0.971)=(79.8\%,\ 97.1\%)[/tex]
Hence, 95% confidence interval for population proportion= [tex](79.8\%,\ 97.1\%)[/tex]
