Refer to the previous exercise. For the null hypothesis, H0: 1 = 2, show that t

Question

Refer to the previous exercise.

For the null hypothesis, H0: 1 = 2, show that

t = 2.62 and the two-sided P@value = 0.059. Interpret.

What decision would you make in the test, using a (i) 0.05 and (ii) 0.10 significance level? Explain

A clinical psychologist wants to choose between two therapies for treating severe cases of mental depression. She selects six patients who are similar in their depressive symptoms and in their overall quality of health. She randomly selects three of the patients to receive Therapy 1, and the other three receive Therapy 2. She selects small samples for ethical reasons— if her experiment indicates that one therapy is superior, she will use that therapy on all her other depression patients. After one month of treatment, the improvement in each patient is measured by the change in a score for measuring severity of mental depression. The higher the score, the better. The improvement scores are Therapy 1: 30, 45, 45 Therapy 2: 10, 20, 30 Analyze these data (you can use software, if you wish), assuming equal population standard deviations. a. Showthatx1 = 40,x2 = 20,s = 9.35,se = 7.64, df = 4, and a 95% confidence interval comparing the means is (-1.2, 41.2).

Explanation / Answer

Null Hypothesis:

H0: µ1 = µ2

Alternative Hypothesis:

H1: µ1 not equal µ2

Test Statistics:

t = 2.62

P-value = 0.059

( i ) 0.05

Here the P-value is greater than (0.059>0.05) the level of significance we fail to reject the null hypothesis.

( ii ) 0.10

Here the P-value is less than the level of significance (0.059 <0.1) we reject the null hypothesis.

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