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Let T have a (Student's) t distribution with 10 degrees of freedom. If P(T < k)...

Let T have a (Student's) t distribution with 10 degrees of freedom. If P(T < k) = 0.95, what is the value of k? Let mu be the unknown mean of a Normal distribution. I take 20 observations randomly from this distribution, and want to test H0: mu = 15 vs H1: mu is not equal to 15 at the 5% level of significance. If I observe a p-value of 0.11, what decision can I make?

Write mu for the mean of a Normal distribution. The value of the standard deviation is unknown. We want to test H0: mu = 8 vs H1: mu > 8. A random sample of 15 observations is taken from this distribution, and the sample mean (x-bar) and sample standard deviation (s) are calculated. Then t = (x-bar - 8)/[s/square_root(15)] is calculated, and is found to equal = 1.85. At what levels of significance could we reject H0?

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