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photoshop1234 [79]
3 years ago
8

Large Sample Proportion Problem. A survey was conducted in Ohio on high school marijuana use. Of the 2266 high school students s

urveyed, 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?
Mathematics
1 answer:
Airida [17]3 years ago
5 0

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

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