SOLUTION: Guests travelling on two different airlines (West Fly Airlines and Air Cosmos) were surveyed for their satisfaction levels of the services offered. 123 of 180 guests travelling by

Question 1132071: Guests travelling on two different airlines (West Fly Airlines and Air Cosmos) were surveyed for their satisfaction levels of the services offered. 123 of 180 guests travelling by West Fly and 157 of the 200 guests travelling by Air Cosmos rates the respective airlines high on service quality. Do the data provide enough evidence to infer that there is no significant difference between the service qualities of the two airline companies? (Use 5% los)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is a two sample proportion
use z, critical value |z|>1.96
(p hat-p)/sqrt(p*(1-p)/n)), where n = (1/n1)+(1/n2)
the two proportions are 0.683 and 0.785
their difference is -0.102
divide by SE, using combined proportion of 280/380, or 0.737, so SE is sqrt (0.737*0.263)((1/180)+(1/200))
=0.045. This approach pools the two proportions, which is reasonable if the null hypothesis says they are equal, therefore part of the same population.
the z value is 2.27 so reject Ho and conclude the two proportions are different.

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