Question 599532: it is thought that a normal population's mean is less than 75. To test this, a random sample of size 19 is drawn. THe sample mean is 73.5 and the sample standard deviation is 2.1. Find an approximate range for the p-value and state the conclusion. What would your range be if we had used a two-tail test?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! it is thought that a normal population's mean is less than 75. To test this, a random sample of size 19 is drawn. THe sample mean is 73.5 and the sample standard deviation is 2.1. Find an approximate range for the p-value and state the conclusion. What would your range be if we had used a two-tail test?
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Ho: u >= 75
Ha: u < 75 (claim)
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Test stat: t(73.5) = (73.5-75)/[2.1/sqrt(19)] = -3.1135
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p(value) = P(t < -3.1135 when df = 18) = 0.0030
Since the p-value is < 5%, reject Ho at the 5% significance level.
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If a 2-tail test, p-value = 2*0.0030 = 0.0060
We would still reject Ho.
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Note: The test results support the claim.
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Cheers,
Stan H.
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