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Problem 1: The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. The file BusinessTravel.xlsx contains a sample of 12 flights with their domestic airfares shown for both years. Has there been a significant increase? µ 1: Current year. H O: µ1 - µ2 ≤ 0 µ 2: Previous year. H a: µ1 - µ2 > 0 Confidence level of 95% = α = 0.05 1= 487 2= 464 Sx 1= 152.4401 Sx 2= 136.0461 N 1= 12 N 2= 12 T= 0.389 Df:22 µ1 > µ2 Since 0.35 > 0.05 Failed to reject H O we can conclude that there is no significant evidence of increasing in airfare. We evaluated a random sample of 12 flights for the current and previous year. According to the file, we could find an average of current airfare 487 with the standard deviation of 152.4401522 and previous year airfare 464 with the standard deviation of 136.0461152. we used a 2sample t-test and the results indicate that with 95% confidence. we can conclude that there has been an insignificant increase between the current and previous year.
Problem 2: You have been asked to evaluate if Houston has higher average hotel rates than Atlanta. The data file Hotel.xlsx contains two random samples of hotel prices. Is there sufficient evidence to conclude that Houston has higher hotel rates? µ 1: Atlanta. H O: µ1 - µ2 ≥ 0 µ 2: Houston. H a: µ1 - µ2 < 0 Confidence level of 95% = α = 0.05 1= 91.71429 2= 101.125 Sx 1= 21.10697 Sx 2= 24.94834 N 1= 35 N 2= 40 µ 1< µ 2 T= -1.7496 P-value= 0.042 df=73 since P-value < 0.05 Reject H O we can conclude that Houston has higher rates. We evaluated a random sample 35 of Atlanta hotel and 40 of Houston. According to the file, we could find an average hotel price of Atlanta was 91.714 with standard deviation 21.10697 and Houston 101.125 with the standard deviation of 24.94834. We used a 2 sample- t-test and the result indicate that with 95% confidence. We can conclude that Houston has higher hotel rates.
Problem 3: An automobile insurance company selected samples of single and married male policy holders and recorded the number who made an insurance claim over the preceding three year period. Of 400 single male policy holders, 76 had made claims while of 900 married male policyholders, 90 had made claims. Do we have sufficient evidence to conclude that married male policy holders make fewer claims? P 1: Single H O: P 1 ≤ P 2 P 2: Married H a: P 1 > P 2 Confidence level of 95% = α = 0.05 X 1 :76 X 2 :90 N 1 :400 N 2 :900 P 1 > P 2 Z=4.4875 P-value=0 Since P-value <0.05 Reject H O We have sufficient evidence to conclude that married male policy holders make fewer claims. We evaluated a random sample of 76 selected from 400 single male and 90 selected of 900 married male. The samples were collected from three year period. We used 2-Prop z- test and the results indicate that with 95%confidence. We can conclude that the married male policyholders make fewer claims.
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