To begin this discussion, suppose you are running a hypothesis test for a popula

Question

To begin this discussion, suppose you are running a hypothesis test for a population mean with the following settings.

H0: ??50H0: ??50 and H1: ?>50H1: ?>50

?=0.05?=0.05

a. What kind of value of the sample mean would justify the outcome of “Reject the null hypothesis”? Explain. (You don’t need to be specific about a precise value of the sample mean, but just provide a general idea of what kind of “evidence” is required to reject the null hypothesis.)

b. Describe how to determine the outcome of a hypothesis test using the P-value. (Again, no specific values are needed here, just a general idea of how the process goes.)

c. Describe how to determine the outcome of a hypothesis test using the rejection region. (Again, no specific values are needed here, just a general idea of how the process goes.)

d. Assume that, in fact, the population mean is equal to 50. If the result of the hypothesis test is to “Reject the null hypothesis”, then an error has just occurred.

i. Explain why this is an error.

ii. What specific type of error is it (Type 1 or Type 2)?

iii. How often will a hypothesis test with the settings above result in this kind of error? Explain.

Explanation / Answer

Answer to part a)

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Answer to part b)

P value is the chance of the null hypothesis to be true, the larger it is the more are the chances of the null to be true, and more difficult it is to reject the same.

There are a couple of decision rules used for the P value analysis:

Rule 1 : If the P value is less than the significance level of the test , we reject the null hypothesis

P value < Alpha, reject

Rule 2: if the P value is more than the significance level of the test, we fail to reject the null hypothesis

P value > alpha , Fail to reject

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Answer to part c)

Rejection region is defined by the Critical values. There are three cases:

Left tailed test: In left tailed test the critical value is negative. The rejection region comes in under the left tail of the normal distribution. If the T statistic < T critical (both have minus sign) then the T statistic falls in the rejection region and we are bound to reject the null

Right tailed test: In right tailed test the critical value is positive. The rejection region comes under the right tail of the normal distribution. If the T statistic > T critical ( both the values have positive sign) then the T statistic falls in the rejection region and we are bound to reject the null

Two tailed test: In two tailed test we have a positive and negative Critical value. In case if the T statistic is positive and it comes under the right tailed rejection region , we reject the null , or in case if the T statistic is negative ans it comes under the left tailed rejection region , we reject the null. Thus in two tailed test there are two rejection regions.

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Answer to part d)

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