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 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.     Treatment Placebo   μ μ1 μ2 n 26 32 x 2.38 2.63 s 0.85 0.57 a. Test the claim that the two samples are from populations with the same mean.   What are the null and alternative​ hypotheses?     A. H0​: μ1<μ2 H1​: μ1≥μ2   B. H0​: μ1=μ2 H1​: μ1≠μ2 Your answer is correct.   C. H0​: μ1=μ2 H1​: μ1>μ2   D. H0​: μ1≠μ2 H1​: μ1<μ2 The test​ statistic, t, is negative 1.28−1.28. ​(Round to two decimal places as​ needed.) The​ P-value is 0.2060.206. ​(Round to three decimal places as​ needed.) State the conclusion for the test.     A. Fail to 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. Your answer is correct.   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.   C. 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.   D. 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. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.   ?<μ1−μ2? ​(Round to three decimal places as​ needed.) Please demonstrate how to use a calculator for this part of the problem i need to learn

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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 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.
 
 
Treatment
Placebo
 
μ
μ1
μ2
n
26
32
x
2.38
2.63
s
0.85
0.57
a. Test the claim that the two samples are from populations with the same mean.
 
What are the null and alternative​ hypotheses?
 
 
A.
H0​:
μ1<μ2
H1​:
μ1≥μ2
 
B.
H0​:
μ1=μ2
H1​:
μ1≠μ2
Your answer is correct.
 
C.
H0​:
μ1=μ2
H1​:
μ1>μ2
 
D.
H0​:
μ1≠μ2
H1​:
μ1<μ2
The test​ statistic, t, is
negative 1.28−1.28.
​(Round to two decimal places as​ needed.)
The​ P-value is
0.2060.206.
​(Round to three decimal places as​ needed.)
State the conclusion for the test.
 
 
A.
Fail to 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.
Your answer is correct.
 
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.
 
C.
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.
 
D.
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. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.
 
?<μ1−μ2<??
​(Round to three decimal places as​ needed.) Please demonstrate how to use a calculator for this part of the problem i need to learn
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