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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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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