1- Explain how to find critical value for a t-distribution? 2- How to determine

Question

1- Explain how to find critical value for a t-distribution?
2- How to determine if two events are mutually exclusive?

3 -Explain the difference between the z-test for the mean using the rejection region and the z-test for the mean using the P-Value? 1- Explain how to find critical value for a t-distribution?
2- How to determine if two events are mutually exclusive?

3 -Explain the difference between the z-test for the mean using the rejection region and the z-test for the mean using the P-Value?
2- How to determine if two events are mutually exclusive?

3 -Explain the difference between the z-test for the mean using the rejection region and the z-test for the mean using the P-Value? 2- How to determine if two events are mutually exclusive?

3 -Explain the difference between the z-test for the mean using the rejection region and the z-test for the mean using the P-Value?

Explanation / Answer

Answer

Part (a)

OR

with example process is shown below

To find a p value (which corresponds to an area under the curve, usually one or both tails of the distribution), we take the integral of this function.

For example, for a t ratio with 10 df, obtained t = 1.70, a mathematician would first evaluate that function for 10 df. To find the one-tailed p value (area of the distribution that lies above 1.70), she/he would integrate the function for the range of values from 1.70 to infinity.

The critical value tables are obtained by working the problem backwards, that is: find the value of t such that the corresponding tail area is .05, .01, .001 and so forth.

Obviously that is more work than applied statisticians want to have to do every time they want a p value. Tables of p values (areas) that were obtained from these integrals have been published for many different df values, for one and two tailed tests, and for different values of p (or alpha).

In addition, there are now many applets or programs on the web that can be used to obtain a p value that corresponds to any obtained value of t.

When people run programs such as SPSS, these programs provide the p values.

The p values for other distributions (such as F and chi squared and others) are obtained in a similar way.

Part (b)

Please signifies what is to be determined when two eventa are mutually exclusive.

Part (c)

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