Question

Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266 high school students surveyed, 970 admitted to smoking marijuana at least once.  A study done 10 years earlier estimated that 45% of the students had tried marijuana. We want to conduct a hypothesis test to see if the true proportion of high school students who tried marijuana is now less than 45%.   Use alpha = .01.
What is the critical value for this test?

Group of answer choices

-1.96

-2.576

-2.33

2.33

Answer 1

Solution:

Given:

Sample size = n= 2266

x = Number of   high school students  admitted to smoking marijuana at least once = 970

Level of significance = 0.01

We have to find the the critical value for this test.

We have to test to see if the true proportion of high school students who tried marijuana is now less than 45%.

Thus this is left tailed test.

look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33.

Thus correct answer is : -2.33