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1. Consider the following hypothesis test Ho: µ = μ。 against H₂: µ ‡ µ。, α = αo when the population variance is known. We said that any value of X between Xtoosmall and Xtoobig would not cause you to get suspicious and reject the null hypothesis, but any value outside this range would cause you to do so. We showed in class that if X is bigger thanx toobig by just the tiniest amount, the confidence interval for the population mean will not include the value μo. This would cause us to reject the null hypothesis. Show that if X is smaller than X toosmall by just the tiniest amount, the confidence interval for the population mean will also not include the value μo,thus causing us also to reject the null hypothesis.

1. Consider the following hypothesis test Ho: µ = μ。 against H₂: µ ‡ µ。, α = αo when the population variance is known. We said that any value of X between Xtoosmall and Xtoobig would not cause you to get suspicious and reject the null hypothesis, but any value outside this range would cause you to do so. We showed in class that if X is bigger thanx toobig by just the tiniest amount, the confidence interval for the population mean will not include the value μo. This would cause us to reject the null hypothesis. Show that if X is smaller than X toosmall by just the tiniest amount, the confidence interval for the population mean will also not include the value μo,thus causing us also to reject the null hypothesis.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 4E
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1. Consider the following hypothesis test Ho: µ = μ。 against H₂: µ ‡ µ。, α = αo when the population variance is known. We said that any value of X between Xtoosmall and Xtoobig would not cause you to get suspicious and reject the null hypothesis, but any value outside this range would cause you to do so. We showed in class that if X is bigger thanx toobig by just the tiniest amount, the confidence interval for the population mean will not include the value μo. This would cause us to reject the null hypothesis. Show that if X is smaller than X toosmall by just the tiniest amount, the confidence interval for the population mean will also not include the value μo,thus causing us also to reject the null hypothesis.
Transcribed Image Text:1. Consider the following hypothesis test Ho: µ = μ。 against H₂: µ ‡ µ。, α = αo when the population variance is known. We said that any value of X between Xtoosmall and Xtoobig would not cause you to get suspicious and reject the null hypothesis, but any value outside this range would cause you to do so. We showed in class that if X is bigger thanx toobig by just the tiniest amount, the confidence interval for the population mean will not include the value μo. This would cause us to reject the null hypothesis. Show that if X is smaller than X toosmall by just the tiniest amount, the confidence interval for the population mean will also not include the value μo,thus causing us also to reject the null hypothesis.
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