Assume that you have a sample of n1= 7​,with the sample mean X1= 41​, and a sample standard deviation of S1= 7, and you have an independent sample of n2= 5 from another population with a sample mean of X2= 33 and the sample standard deviation S2= 8. Assuming the population variances are​ equal, at the 0.01 level of​ significance, is here evidence that H1​:μ1>μ2​? Part 1 a. Determine the hypotheses. Choose the correct answer below. A. H0​:μ1≠μ2H1​:μ1=μ2 B.H0​:μ1≤μ2H1​:μ1>μ2

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Assume that you have a sample of n1= 7​,with the sample mean X1= 41​, and a sample standard deviation of S1= 7, and you have an independent sample of n2= 5 from another population with a sample mean of X2= 33 and the sample standard deviation S2= 8. Assuming the population variances are​ equal, at the 0.01 level of​ significance, is here evidence that H1​:μ1>μ2​?
Part 1
a. Determine the hypotheses. Choose the correct answer below.
A. H0​:μ1≠μ2H1​:μ1=μ2
B.H0​:μ1≤μ2H1​:μ1>μ2
C.H0​:μ1>μ2H1​:μ1≤μ2
D.H0​:μ1=μ2H1​:μ1≠μ2
 
b. Compute the pooled variance. ​(Round to three decimal places to the right of the decimal point as​ needed.)
A.
S2p = [(7−1)•(7)]2+([5−1)•(8)]2(7−1)+(5−1) = 278810 = 278.8​, using formula​ (10.1)
B.
S2p = (7−1)•(7)+(5−1)•(8)(7−1)+(5−1) = 7410 = 7.4​, using formula​ (10.1)
C.
S2p = (7−1)•(7)2+(5−1)•(8)2(7−1)+(5−1) = 55010 = 55​, using formula​ (10.1)
D.
p = (41 + 33)(7 + 5) =7412= 6.167​, using formula​ (10.5)
 
c. Then using the pooled​ variance, compute the test statistic.​ (Round to two decimal places to the right of the decimal point as​ needed.)
A.
tSTAT = (33 − 41)278.8 • 15+17 = −895.589= −0.82, using formula​ (10.1)
 
B.
tSTAT = (41 − 33)7.4 • 17+15 = 82.537= +5.02​, using formula​ (10.1)
 
C.
tSTAT = (41 − 33)55 • 17+15 = 818.857= +1.84​, using formula​ (10.1)
 
D.
ZSTAT = (41 − 33)[6.167 • (1− 6.167)] 17+15 = 8−10.925= +2.42​, using formula​ (10.5)
 
d. Determine the​ p-value. ​(Round to three decimal places as​ needed.)
 
 
 
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