Answer to Question #305500 in Statistics and Probability for marky boy

Question

The school registrar estimates that the dropout rate of freshmen high schools in Mindanao

is 20%. Last year, 45 freshmen from a random sample of 250 Mindanao freshmen high

school withdrew. At 𝛼 = 0.01, is there enough evidence to reject the registrar’s claim?

Answer 1

$H_0:p=p_0=0.2$

$H_1:p\not=0.2$

Test statistics

$T={\frac {{\frac m n}-p_0} {p_0*(1-p_0)}}*\sqrt{n}$ , where m - number of satisfiyung observations, n - sample size

In the given case we have

$T={\frac {{\frac {45} {250}}-0.2} {0.2*0.8}}*\sqrt{250}\approx -1.98$

Since the sample size is big(>30), then it is appropriate to use z-score as critical value C, so, since we run two-tailed test

$P(Z>C)={\frac {0.01} 2}=0.005\implies C=2.58$

Since $T\in(-2.58,2.58)$ , then we should accept the null hypothesis and conclude that, based on the data, there is no statisticsal evidence at $\alpha=0.01$ to conclude that $p\not=0.2$