Question 1112788: Residents of Hawkins, Indiana, believe something has stunted the growth of adult males. Let µ = average height of an adult male born in Hawkins, Indiana. The city wants to test Ho: µ = 69 inches against Ha: µ ≠ 69 inches. A random sample of 16 males born in Hawkins yields xbar = 66.5 and s = 4. For α = 0.05, what do you conclude? Assume the relevant population follows a normal random variable.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Residents of Hawkins, Indiana, believe something has stunted the growth of adult males. Let µ = average height of an adult male born in Hawkins, Indiana. The city wants to test Ho: µ = 69 inches against Ha: µ ≠ 69 inches. A random sample of 16 males born in Hawkins yields xbar = 66.5 and s = 4. For α = 0.05, what do you conclude? Assume the relevant population follows a normal random variable.
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z(66.5) = (66.5-69)/4 = -2.5/4 = -0.625
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p-value = 2P(z < -0.625) = 2*normalcdf(-100,-0.625) = 0.5320
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Since the p-value is greater than 5%, fail to reject Ho.
The results support the claim that u = 69 inches.
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Note:: I assumed your s = 4 referred to the sample, not the population.
If s=4 refers to the population z = -2.5/(4/sqrt(16)) = -2.5
THEN the p-value would be 2*normalcdf(-100,-2.5) = 2*0.006 = 0.012
Since that p-value is less than 5% you would reject Ho.
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Cheers,
Stan H.
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