Question 1132052: Question 1 The Sales manager at Hybrid Industries a high tech farming agency claims that there has been a drop in the sales from the target of $2800/- per week. Data was collected for the last 48 weeks and the sample mean was computed as $ 2435/- with a s.d. $ 351. Verify at 5% los if the manager’s claim can be accepted based on the sample observations
Question 2 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! Assuming normality, random sample and s being an unbiased estimator of sigma, all that
test statistic is a t 0.975, df=48
critical value |t|>2.01
calculation (x bar-mean)s/sqrt(48)
that is (-365)/351/sqrt(48)
which is -7.20 and strongly reject Ho that the two are equal with p<<0.0001
The second 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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