Due Sat Attempts: Average: 2. Exercise 8.17 (Algorithmic) The International Air

Question

Due Sat Attempts: Average: 2. Exercise 8.17 (Algorithmic) The International Air Transport Association surveys business travelers to develop qualty ratings for transatlantic gateway airports. The maximum possible rating is 10, Suppose a 50 business travelers is elected and each trayeler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 10 3 4S576910 5465 6 410 9 10 61010 Develop a 95% confidence interval estinate of the population mean rating for Mar. Round your answers to two deemal places. Enter your answer using parentheses and a cemma, in the form (n.,n2). De not use commas in your numenical answer (ie use 1200 instead of 1,200, etc)

Explanation / Answer

Solution:

Here, we have to find 95% confidence interval for population mean rating. The confidence interval formula is given as below:

Confidence interval = Xbar -/+ t/2, n – 1*S/sqrt(n)

From the given data, we have

Sample mean = Xbar = 6.76

Sample standard deviation = S = 2.55199002

Sample size = n = 50

Confidence level = c = 95% = 0.95

Significance level = = 1 – c = 1 – 0.95 = 0.05

Degrees of freedom = n – 1 = 50 – 1 = 49

Critical value = t/2, n – 1= 2.0096

(By using t-table or excel)

Confidence interval = Xbar -/+ t/2, n – 1*S/sqrt(n)

Confidence interval = 6.76 -/+ 2.0096* 2.55199002/sqrt(50)

Confidence interval = 6.76 -/+ 2.0096*0.36090589

Confidence interval = 6.76 -/+ 0.7253

Lower limit = 6.76 - 0.7253 = 6.0347

Upper limit = 6.76 + 0.7253 = 7.4853

Confidence interval = (6.03, 7.49)

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