Question 1066038: A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means?
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Ho: u1-u2 = 0
Ha: u1-u2 # 0
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x-bar = (23-26) = -3
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t(-3) = (-3-0)/sqrt[(4^2/10)+(5^2/8)] = -3/2.1737 = -1.3801
df = n2-1 = 7
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p-value = 2*P(-100< t < -1.3801) = 2*tcdf(-100,-1.3801,7) = 0.2100
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Since the p-value is greater than 5%, fail to reject Ho.l
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Conclusion:: The two means are statistically equal at the
5% significance level.
Cheers,
Stan H.
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