Question 1075959: A medical researcher says that less than 24% of adults in a certain country are smokers. In a random sample of 250 adults from that country, 19.2% say that they are smokers. At alphaαequals=0.05, is there enough evidence to support the researcher's claim?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: There is not enough evidence to say it is not 24% p=0.24
Ha: There is enough evidence p NE 0.24
alpha=0.05 P{reject Ho|Ho true}
test stat is 1 sample proportion
z=(p hat-p)/sqrt(p*(1-p))/n}
critical value abs |z|>1.96
numerator is -0.048
denominator is 0.027
z=-1.78
I fail to reject Ho based on this evidence, p-value is 0.076
Note: if this is set up as a 1-way test, that we have evidence to suggest that if it is not 24% it is very likely to be less, then the critical value would be -1.64 and we would reject Ho. In the absence of that clarification, I would make this a 2-way test and the answer as given above.
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