Let\'s examine the relationship between CI\'s and hypothesis tests: (a) You calc

Question

Let's examine the relationship between CI's and hypothesis tests: (a) You calculate a 90% confidence interval for and come up with (10, 22). If you test H0: = 27 and use = .10, will you reject H0? Why or why not? (b) Now you calculate a 95% CI for and come up with (-3, 6). If you test H0: = 7 and use = .10, will you reject H0? Why or why not? (c) Finally, you calculate a 95% CI for for and come up with (-34, -28). If you test H0: = - 23 and use = .01, will you reject H0? Why or why not? Hint: you need to think about how confidence levels and hypothesis tests are equivalent. In particular, what happens to a CI as you change the confidence level?

Explanation / Answer

Ans:

a)90% CI is (10,22)

As,Confidence interval limits does not include 27,it means that mean is not equal to 27.

So,Reject H0.

b)95% CI is (-3,6)

alpha=0.1 mens 90% confidence level.

90% CI will be narrower that the above given 95% CI and it will not include 7 within limits.

Hence,Reject H0.

c)95% CI is (-34,-28)

Margin of errot=6/2=3

Margin of error for 99% CI=3*2.58/1.96=3.95

99% CI limits are (-34.95,-27.05)

99% will be wider but still not include -23.

So,Reject H0.

As,the confidence level increases,CI becomes wider,as margin or error increases(as z value increases)

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