Question 1112789: 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 rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Null Hypothesis, Ho: u = 69 inches where u is the mean
Alternative Hypothesis, Ha: u not = 69 inches
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standard error = 4/square root(16) = 1
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the test statistic is the z-score, since the population is normally distributed
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z-score = (66.5 - 69) / 1 = -2.5
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since Ha states not =, we have a two tailed test
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a = 0.05 and a/2 = 0.025 and critical probability is 0.975 (1 - (a/2))
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the corresponding z-score for 0.975 is 1.960
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our test statistic is -2.5 so we reject Ho and accept H1
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the test is reject Ho if test statistic is < -1.960 or > 1.960
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