Question

PART I

Researchers in the corporate office of an airline wonder if there is a significant difference between the cost of a flight on Priceline.com vs. the airline's own website. A random sample of 16 flights were tracked on Priceline and the airline's website and the average difference between the vendors was $4.251 with a standard deviation of $9.2763. The 99% confidence paired-t interval for price (Priceline - Airline Site) was (-2.5826, 11.0846). Which of the following is the appropriate interpretation?

	1) We are 99% confident that the average difference in the prices of the flights sampled is between -2.5826 and 11.0846.
	2) We are 99% confident that the average difference in price between the two vendors for all flights is between -2.5826 and 11.0846.
	3) The proportion of all flights that had a difference in price between the two vendors is 99%.
	4) We are 99% confident that the difference between the average price on Priceline and the average price on the airline's website is between -2.5826 and 11.0846.
	5) We are certain the average difference in prices between the two vendors for all flights is between -2.5826 and 11.0846.

PART II

A survey conducted by General Motors of 38 drivers in America, 33 indicated that they would prefer a car with a sunroof over one without. When estimating the proportion of all Americans who would prefer a car with a sunroof over one without with 90% confidence, what is the margin of error?

	1) 0.0702
	2) 0.0899
	3) 0.0146
	4) 0.0548
	5) 0.0049

PART III

A U.S. census bureau pollster noted that in 379 random households surveyed, 218 occupants owned their own home. What is the 99% confidence interval estimate of the proportion of American households who own their own home?

	1) ( 0.51613 , 0.63427 )
	2) ( -0.50979 , 0.6406 )
	3) ( 0.54981 , 0.60059 )
	4) ( 0.3594 , 0.49021 )
	5) ( 0.50979 , 0.6406 )

Answer 1

PART I

99% confidence paired-t interval for price (Priceline - Airline Site) was (-2.5826, 11.0846)

2) We are 99% confident that the average difference in price between the two vendors for all flights is between -2.5826 and 11.0846.

PART II

n = number of drivers in America = 38

x = number of drivers who prefer a car with a sunroof over one = 33

                    (Round to 4 decimal)

Confidence level = c = 0.90

Margin of error (E):

Where zc is z critical value for (1+c)/2 = (1+0.90)/2 = 0.95

zc = 1.645                 (From statistical table of z values, average of 1.64 and 1.65)

E = 1.645 * 0.05484

E = 0.0902                        (Round to 4 decimal)

Margin of error = 0.0902

PART III

n = number of households randomly selected = 379

x = number of occupants who owned their own home = 218

                    (Round to 4 decimal)

Confidence level = c = 0.99

Margin of error (E):

Where zc is z critical value for (1+c)/2 = (1+0.99)/2 = 0.995

zc = 2.58                 (From statistical table of z values)

E = 2.58 * 0.025391

E = 0.0655                 

Margin of error = 0.0655091

99% confidence interval estimate of the proportion of American households who own their own home is

0.5752 - 0.0655091 < p< 0.5752 + 0.0655091

0.50969 < p < 0.64071                   (Round to 4 decimal)

99% confidence interval estimate of the proportion of American households who own their own home is (0.50969, 0.64071)