Randomly selected 20 student cars have ages with a mean of 7.3 years and a standard deviation of 3.4 years, while randomly selected 11 aculty cars have ages with a mean of 5 years and a standard deviation of 3.7 years. b) The test statistic is (c) The p-value is
Data:
n1 = 20
n2 = 11
x1-bar = 7.3
x2-bar = 5
s1 = 3.4
s2 = 3.7
Hypotheses:
Ho: μ1 = μ2
Ha: μ1 ≠ μ2
Decision Rule:
α = 0.05
Degrees of freedom = 20 + 11 - 2 = 29
Lower Critical t- score = -2.045229611
Upper Critical t- score = 2.045229611
Reject Ho if |t| > 2.045229611
Test Statistic:
Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((20 - 1) * 3.4^2 + (11 - 1) * 3.7^2)/(20 + 11 -2)) = 3.506
SE = s * √{(1 /n1) + (1 /n2)} = 3.50634892140253 * √((1/20) + (1/11)) = 1.316208338
t = (x1-bar -x2-bar)/SE = 1.747443724
p- value = 0.091143513
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