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?
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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