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 0.05 significance level for both parts.     Treatment Placebo   μ μ1 μ2 n 27 39 x 2.38 2.65 s 0.87 0.61 a. Test the claim that the two samples are from populations with the same mean.

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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
0.05
significance level for both parts.
 
 
Treatment
Placebo
 
μ
μ1
μ2
n
27
39
x
2.38
2.65
s
0.87
0.61
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
 
C.
H0​:
μ1=μ2
H1​:
μ1>μ2
 
D.
H0​:
μ1=μ2
H1​:
μ1≠μ2
Your answer is correct.
The test​ statistic, t, is
 
​(Round to two decimal places as​ needed.)
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