Will rate We take 61 samples of a random variable that is supposed to have a sta

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Will rate

We take 61 samples of a random variable that is supposed to have a standard normal distribution. We will use the sample data to test whether or not the mean is zero and whether or not the standard deviation (or equivalently, the variance) is equal to 1 (a) First, test the variance o2 1 Hi 02 1. How high or how low does S2 need to be to reject the null hypothesis for an a 0.05? (b) Second, test the mean: Ho: 0, Hi 0. How high or how low does need to be to reject the null hypothesis for an a 0.05? (c) Assume that X and S2 are independent. Given Ho is true, what is the probability that we will see a false alarm in either the test on the variance or the test on the mean?

Explanation / Answer

two common situations:

The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either "Reject H0 in favour of H1" or "Do not reject H0". We never conclude "Reject H1", or even "Accept H1".

If we conclude "Do not reject H0", this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1. Rejecting the null hypothesis then, suggests that the alternative hypothesis may be true.

A one sample t-test is a hypothesis test for answering questions about the mean where the data are a random sample of independent observations from an underlying normal distribution N(

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