Answer to Question #212036 in Statistics and Probability for TIN

Question

 In a public senior high school, a survey conducted last year by the barangay health workers showed that 10% of the students drink alcohol. This year, a new survey was conducted randomly on 320 students from the same school and it was found out that 28 of them drink alcohol. Determine if the claim that there is a decrease on the proportion of senior high school students who drink alcohol is true. Use α = 0.05.

Answer 1

$H0:P=0.1$

$Ha:P<0.1$

$\hat P=0.0875$

$z=\frac{\hat P-P}{\sqrt{\frac{P(1-P)}{n}}}$

$=\frac{0.875-0.1}{\sqrt{\frac{0.1\times 0.9}{320}}}$

$=-0.74536$

$Cv=z_{0.05}=-1.645$

Since the absolute value of the test statistic 0.74536 is less than the absolute value of the critical value, 1.645, we fail to reject the null hypothesis. There is no sufficient evidence to support the claim that there is a decrease on the proportion of senior high school students who drink alcohol.