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If when you do a Hypothesis test about the Population Mean, somehow you have the actual value for the Population Standard Deviation. Suppose that you were able to get a sample of size 100, and did not know the Population Standard Deviation. What can you do to still carry out the Hypothesis test?

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The solution addresses when you do a Hypothesis test about the Population Mean, somehow you have the actual value for the Population Standard Deviation. Suppose that you were able to get a sample of size 100, and did not know the Population Standard Deviation. What can you do to still carry out the Hypothesis test?

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Let's assume that the mean of samples is M, and the Population Mean is m.
Then H0: m = M against H1: m<>M
We will construct the confidence interval of the mean M. If m falls within the interval, we can accept H0; if not, we reject it.
To construct the confidence interval, we should estimate the standard deviation s first. When s is known, the formula:
M - z*s < m < M + z*s
is used for a confidence interval. ...

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