Final answer:
The calculated t statistic for comparing two independent means with the given data is approximately 3.8185.
Step-by-step explanation:
To calculate the t statistic for comparing two independent means where the null hypothesis is H0: μ1 = μ2 and the alternative hypothesis is Ha: μ1 > μ2, you use the following formula:
t = (m1 - m2) / sqrt((s1^2/N1) + (s2^2/N2))
Using the given values:
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- N1 = Number of observations in sample 1 = 10
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- N2 = Number of observations in sample 2 = 10
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- m1 = Mean of sample 1 = 526
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- m2 = Mean of sample 2 = 373.3
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- s1 = Standard deviation of sample 1 = 107
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- s2 = Standard deviation of sample 2 = 67.5
You would substitute these values into the formula:
t = (526 - 373.3) / sqrt((107^2/10) + (67.5^2/10))
After performing the calculations:
t = 152.7 / sqrt((107^2/10) + (67.5^2/10))
t = 152.7 / sqrt((11449/10) + (4556.25/10))
t = 152.7 / sqrt(1144.9 + 455.625)
t = 152.7 / sqrt(1600.525)
t = 152.7 / 40.006
t = 3.8185
The calculated t statistic is approximately 3.8185.