Answer to Question #201526 in Statistics and Probability for ann

Question

In a graduate teacher college, a survey was conducted to determine the proportion of students who want to major in mathematics. If 368 out of 850 students said yes, with 95% confidence, what interpretation can we make regarding the probability that all students in the teacher graduate college want to major in mathematics?

Answer 1

Here,

X = 368

n = 850

$p'=\dfrac{X}{n}=\dfrac{368}{850}=0.433$

95% confidence interval

$So \ \alpha=1-0.95-0.05$

$\implies Z_{\alpha/2}=1.96$

Now, $q'=1-p'=1-0.43=0.57$

and $\sqrt{\dfrac{p'q'}{n}}=\sqrt{\dfrac{0.43\times 0.57}{850}}=0.0169$

for the lower limit:

$p'-Z_{\alpha/2}\sqrt{\dfrac{p'q'}{n}}=0.433-(1.96)(0.0169)=0.396\ or\ 39.6\%$

for the upper limit:

$p'+Z_{\alpha/2}\sqrt{\dfrac{p'q'}{n}}=0.433+(1.96)(0.0169)=0.464\ or\ 46.4\%$

Thus, with 95% confidence, we can state that the interval from 39.6% to 46.4% contains the true percentage of all graduate students who want to major in Mathematics.