Question

In a 1993 survey of 560 college students, 171 said that they used illegal drugs in the past year. In a more recent survey of 720 college students, 263 said that they used illegal drugs during the previous year. We want to know if the evidence supports the claim that the proportion of college students using illegal drugs has increased since 1993 at a 0.05 significance level.

1.Regardless of whether the requirements are met, conduct the appropriate hypothesis test. What is the value of the z test statistic, written to two decimal places?

2.What is the p-value for the z test statistic, written to three decimal places?

Answer 1

solution:

let sample 1 is used for data of recent study and sample no 2 is denoted for data of 1993

for sample 1:

number of students who used drug in recent years =

so

for sample 2:

number of students who used drug in past year in 1993 studty =

value of the pooled proportion is computed as

null and alternative hypothesis:

since it is a right tailed test:

test statistics:

significance level = 0.05

p value = 1- value of z to the left of 0.42 = 1 - 0.6628 = 0.3372

p value = 0.337

since p value > 0.05

, so not rejecting the null hypothesis

conclusion;

there is not enough evidence to say that the proportion of student who say they use drug in past year have increase since 1993.