Question

Do a t-test of sample means differences assuming unequal variance of these grpups. Write hypothesis, scientific findings and “layman” terms. Test at 95% confidence and show all works. Sample 1 - flight times Charlotte To Dallas with Boeing 737 Mean time 206 minutes Variance = 29 minutes Sample size = 41 flights Sample 2 flight times Charlotte To Dallas with Airbus 320 Mean time 201 minutes Variance = 39 minutes Sample size = 67 flights

Answer 1

Data:         

n1 = 41        

n2 = 67        

x1-bar = 206        

x2-bar = 201        

s1 = 5.385164807        

s2 = 6.244997998        

Hypotheses:         

Ho: μ1 = μ2         

Ha: μ1 ≠ μ2         

Decision Rule:         

α = 0.05        

Degrees of freedom = 41 + 67 - 2 = 106       

Lower Critical t- score = -1.982597204        

Upper Critical t- score = 1.982597204        

Reject Ho if |t| > 1.982597204        

Test Statistic:         

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =   √(((41 - 1) * 5.3851648071345^2 + (67 - 1) * 6.2449979983984^2)/(41 + 67 -2)) =   5.935

SE = s * √{(1 /n1) + (1 /n2)} = 5.93518450381617 * √((1/41) + (1/67)) = 1.176838241       

t = (x1-bar -x2-bar)/SE = 4.248672269        

p- value = 4.63543E-05        

Decision (in terms of the hypotheses):         

Since 4.248672269 > 1.982597204 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence of a significant difference between the mean times.