Question 1181945: A local government official claims that only up to 25% of all public school students in the city own an electronic gadget that can be used for distance learning like a cellphone, tablet, or laptop. To test the claim, a group of Grade 11 Statistics students made a survey and found out that out of 1,000 randomly selected students, 275 indicated that they are ready for Online learning. Can we infer from the data that the local official is true to his claim? Set up the Rejection Region and the Critical Values for Left-Tailed, Right-Tailed, and Two-Tailed tests. Use ɑ=.01
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: p=0.25
Ha: p NE 0.25
alpha=0.01 p{reject Ho|Ho true}
test is a z, reject if |z| > 2.576. That is the rejection region for a two way test.
For a 1-way right-tailed test the rejection region would be z>2.326
for a 1-way left-tailed test, the data themselves show a proportion that is not below the mean.
z=(0.275-0.25)/sqrt(0.25*0.75/1000)
=0.025/0.137
=1.826
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Fail to reject Ho at the 0.01 level two way test and right-tail test. Insufficient evidence exists to counter the official's claim.
It was rejected a priori for a left-tail test.
p-value = 0.0679
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