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- Apr 14, 2013

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We have the following hypotheses: $$H_0: \mu\geq 60 \ \ \ , \ \ \ H_1:\mu<60$$

A test is executed with a sample of size $25$ and an estimated standard deviation $S'=8$.

From the test we get a p-value of 5%. I want to determine the value of the mean of the sample $\overline{X}$.

The p-value is equal to $P(T\leq t\mid H_0)$. So is this in this case equal to

$P(\mu\leq 60\mid H_0)$ ?

If yes, then we have the following: $$p=0.05\Rightarrow \Phi \left (\frac{\overline{X}-60}{\frac{S'}{\sqrt{n}}}\right )=0.05 \Rightarrow \Phi \left (\frac{\overline{X}-60}{\frac{8}{\sqrt{25}}}\right )=0.05\Rightarrow \frac{\overline{X}-60}{\frac{8}{\sqrt{25}}}=\Phi^{-1}(0.05)$$ Or am I thinking wrong?

Do we use here the table of t-distribution?