Question

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 69 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance.

Answer 1

Answer:

There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

Step-by-step explanation:

Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.

Let p1 be the proportion of local seniors and p2 national seniors.

$H_0: p_1=p_2\\H_a: p_1 >p_2$

(right tailed test at 5% significance level)

Group I II  

Success 69 60 129

Total 100 100 200

p 0.69 0.6 0.645

q 0.31 0.4 0.355

se 0.046249324 0.048989795 0.033836002

p diff 0.09  

Std error 0.03384  

Z 2.659574468 0  

p 0.00391  

we find that p value is 0.00391 <0.05

Hence we reject null hypothesis

There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.