Question 595828: A researcher believes that most swimming champions are men. He collects the names and sexes of the past 20 all-time swimming champions in the US. He finds that 16 of them are men. However, it is also well-known that 70% of professional swimmers are men.
a. What is the probability that out of 20 swimming champions, 16 of them are men?
b. What is the critical value to test our hypothesis using an alpha level of .05?
c. What is the critical value (in terms of # of men) if our alpha level was .01?
d. What is the p-value for the researcher’s observed outcome?
e. Make a decision about the researcher’s hypothesis, using an alpha level of .01.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A researcher believes that most swimming champions are men. He collects the names and sexes of the past 20 all-time swimming champions in the US. He finds that 16 of them are men. However, it is also well-known that 70% of professional swimmers are men.
a. What is the probability that out of 20 swimming champions, 16 of them are men?
P(x = 16) = 20C16*(1/2)^16*(1/2)^4 = 0.0046
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b. What is the critical value to test our hypothesis using an alpha level of .05?
Ho: p(men) <= 1/2
Ha: p(men) > 1/2 (claim)
Critical value z = 1.645
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c. What is the critical value (in terms of # of men) if our alpha level was .01?
Crical value: z = 2.3263
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d. What is the p-value for the researcher’s observed outcome?
p-hat = 16/20 = 0.8
z(0.8) = (0.8-0.5)/sqrt[0.5*0.5/20] = 2.6833
p-value = P(z > 2.6833) = 0.0036
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e. Make a decision about the researcher’s hypothesis, using an alpha level of .01.
Since the p-value is less than 0.01, reject Ho.
The data supports the claim.
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Cheers,
Stan H.
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