Question

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 cost of the same flight on the airline's own website. A random sample of 6 flights were tracked on Priceline.com and the airline's website and the mean difference in price (Priceline.com - Airline Site) was $-51.971 with a standard deviation of $11.1065. Create a 99% confidence interval for the true average difference in costs between the vendors.

Question 5 options:

1)	(-56.0031, -47.9389)

2)	(-68.7813, -35.1607)

3)	(-56.5052, -47.4368)

4)	(70.2536, -33.6884)

5)	(-70.2536, -33.6884)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = -51.971

sample standard deviation = s = 11.1065

sample size = n = 6

Degrees of freedom = df = n - 1 = 6-1 = 5

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

t/2,df = t_{0.005,5 = 4.03}

t _/2,df = 4.03

Margin of error = E = t_/2,df * (s /n)

= 4.03 * (11.1065 / 6)

Margin of error = E = 18.28258

The 99% confidence interval estimate of the population mean is,

- E < < + E

-51.971- 18.28258 < < -51.971 + 18.28258

-70.2536 < < - 33.6884

( -70.2536,- 33.6884)

Answer = 5) ( -70.2536,- 33.6884)