I need the last part answered and the steps to find the answer A study was done

Question

I need the last part answered and the steps to find the answer

A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent H1 H2 simple random samples selected from normally distributed populations. and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below Use a 0.01 significance level for both parts. 238 267 s 0.88 0.53 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? The test statistic t is 1.45 (Round to two decimal places as needed The P-value is .153 (Round to three decimal places as needed.) State the conclusion for the test. O A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. CM C. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection ofthe claim that the two samples are from populations with the same mean. O D. Reject the nullhypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. (Round to three decimal places as needed.)

Explanation / Answer

Confidence Interval:

(x1 bar – x2 bar ) (-/+) E

E = tc *SE

SE = sqrt ((s1^2/n1)+(s2^2/n2))

To find tc (critical t value) we need to find the degrees of freedom. We can calculate the degrees of freedom by using the following formula:

df = ((n1-1)*(n2-1))/(((n2-1)*c^2)+((n1-1)*(1-c^2))

c = (s1^2/n1)/((s1^2/n1)+(s2^2/n2))

n1 = 25

n2 = 32

s1 = 0.88

s2 = 0.53

x1 bar = 2.38

x2 bar = 2.67

SE = sqrt ((0.88^2/25)+(0.53^2/32))

     = 0.1994

c = (0.88^2/25)/((0.88^2/25)+(0.53^2/32))

= 0.7792

df = ((25-1)*(32-1))/(((32-1)*0.7792^2))+((25-1)*(1-0.7792^2))

    = 26

Now for 26 degrees of freedom at 1% level of significance the critical t is given in table as 2.779

E = 2.779 * 0.1994

   = 0.5541

x1 bar – x2 bar = 2.38 – 2.67

                           = -0.29

(x1 bar – x2 bar ) (-/+) E

(-0.29) (-/+) 0.5541

-0.844 and 0.264

Answer:

-0.844 < µ1 - µ2 < 0.264

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