Question

Large Sample Proportion Problem. A survey was conducted in Ohio on high school marijuana use. Of the 2266 high school students surveyed, 952 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 in Ohio who tried marijuana is now less than 45%. Use alpha = .01.
What is the standard error for this test?

Answer 1

Answer: 0.0328

Step-by-step explanation:

Standard error is the standard deviation of the sampling distribution.

The formula to find the standard error is given by :-

$SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

,where n= sample size.

$\hat{p}$= Sample proportion.

Given : Of the 2266 high school students surveyed, 952 admitted to smoking marijuana at least once.

A study done 10 years earlier estimated that 45% of the students had tried marijuana.

i.e. Population proportion : p= 0.45

Sample size : n= 226

Sample proportion : $\hat{p}=\dfrac{952}{2256}\approx0.42$

Then , the standard error for this test will be :-

$SE=\sqrt{\dfrac{0.42(1-0.42)}{226}}\\\\ SE=\sqrt{0.0010779}=0.0328310\approx0.0328$

Hence, the  standard error for this test= 0.0328