SOLUTION: A medical researcher says that at least 23% of adults are smokers. In a random sample 250 adults, 22.4% say they are smokers. At alpha=0.03, is there enough evidence to the reject

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Question 780109: A medical researcher says that at least 23% of adults are smokers. In a random sample 250 adults, 22.4% say they are smokers. At alpha=0.03, is there enough evidence to the reject the researcher's claim? What is critical value of zo? What is the standardized test static? What would be the correct conclusion of the test? Fail to reject or reject?

Found 2 solutions by reviewermath, stanbon:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
A medical researcher says that at least 23% of adults are smokers. In a random sample 250 adults, 22.4% say they are smokers. At alpha=0.03, is there enough evidence to the reject the researcher's claim? What is critical value of zo? What is the standardized test static? What would be the correct conclusion of the test? Fail to reject or reject?
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A:
Null Hypothesis, H%5B0%5D: p ≥ 0.23
Alternative Hypothesis, H%5B1%5D: p < 0.23
α = 0.03
Critical Value: z%5B.03%5D = -1.8808
Test Stat: z = %280.224-0.23%29%2Fsqrt%280.23%2A%281-0.23%29%2F250%29 = -0.2254
Fail to reject H%5B0%5D because the test statistic is NOT lower than the critical value. Sample does NOT provide enough evidence to reject the medical researcher's claim.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A medical researcher says that at least 23% of adults are smokers.
Ho: p <= 0.23
Ha: p > 0.23 (claim)
p-hat = 0.224
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In a random sample 250 adults, 22.4% say they are smokers.
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What is the standardized test static?
z(0.224) = (0.224-0.23)/sqrt(0.23*0.77/250) = -0.2254
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At alpha=0.03, what is critical value of zo?
invNorm(0.03) = -1.8808
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At alpha=0.03, is there enough evidence to reject the researcher's claim?
Ans: No
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What would be the correct conclusion of the test? Fail to reject or reject?
Fail to reject.
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Cheers,
Stan H.
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