eBook {Exercise 8.17 Algorithmic} The International Air Transport Association su

Question

eBook {Exercise 8.17 Algorithmic} The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 5 9 10 2 2 2 2 7 77 6 7 8 99 2 10 2 7 6 9 8 109 2 75 7 2 2 7 7 6 2 10 695 2 10 7 10 2 2 6 Develop a 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

Explanation / Answer

Sol:

Find mean

find sd

df=n-1=50-1=49

tcrit =2.0095

Then find the confidence interval by

sample mean-zcrit(samplesd/sqrt(n),sample mean+zcrit(samplesd/sqrt(n)

,Compute mean and sd in R

code is:miami <-c(5,9,10,2,2,2,2,7,7,7,7,6,7,8,9,9,2,10,2,7,6,9,8,10,9,2,7,5,7,2,2,7,7,6,2,10,8,2,6,6,9,5,2,10,7,10,2,2,6,6)
mean(miami)
sd(miami)

output:

> mean(miami)
[1] 6
> sd(miami)
2.857143

95% confidence interval is

6-2.0095(2.857143)/sqrt(50),6+2.0095(2.857143)/sqrt(50)

5.19,6.81

USED T CRITICAL

95% confidence interval estimate for the population mean rating for Miami lies in between

5.19and 6.81

USING R CODE ALSO I GOT SAME ANSWER:

miami <-c(5,9,10,2,2,2,2,7,7,7,7,6,7,8,9,9,2,10,2,7,6,9,8,10,9,2,7,5,7,2,2,7,7,6,2,10,8,2,6,6,9,5,2,10,7,10,2,2,6,6)
mean(miami)
sd(miami)
print(miami)
t.test(miami)

OUTPUT:

One Sample t-test

data: miami

t = 14.849, df = 49, p-value < 2.2e-16

alternative hypothesis: true mean is not equal to 0

95 percent confidence interval:

5.188009 6.811991

sample estimates:

mean of x

6

ANSWERS IN BOLD

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