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?

Answer 1

Null Hypothesis H0: True proportion of high school students who tried marijuana is 45%. That is p = 0.45

Alternative Hypothesis Ha: True proportion of high school students who tried marijuana is less than 45%. That is p < 0.45

Sample proportion = 970 / 2266 = 0.4281

Standard error of sample proportion, se =

For one sided left tail test and alpha = .01, the critical values of Z is -2.33. That is, we reject the null hypothesis if Z < -2.33

Test statistic, Z = ( - p) / se

= (0.4281 - 0.45) / 0.01045

= -2.096

As, the observed Z is greater than the critical value of -2.33, we fail to reject the null hypothesis and conclude that there is not significant evidence that true proportion of high school students who tried marijuana is less than 45%.