The travel website ‘Hotwire’ specializes in searching for and aggregating the co
ID: 3131227 • Letter: T
Question
The travel website ‘Hotwire’ specializes in searching for and aggregating the costs of various types of reservations such as car rentals, flights, and hotels. Travel websites compete, among other things, on the speed with which their search engines can provide the results to a web query. Suppose that Hotwire has just hired a series of hotshot database and programming wizards to improve their query search times. We record the search time for 300 randomly selected car rental searches. The sample statistics are: sample mean = 7.332 seconds and sample standard deviation = 2.073 seconds. Give your answer as a properly formatted confidence interval statement. Choose the “standard” value for C.
Explanation / Answer
Confidence Interval
The travel website ‘Hotwire’ specializes in searching for and aggregating the costs of various types of reservations such as car rentals, flights, and hotels. Travel websites compete, among other things, on the speed with which their search engines can provide the results to a web query. Suppose that Hotwire has just hired a series of hotshot database and programming wizards to improve their query search times. We record the search time for 300 randomly selected car rental searches. The sample statistics are: sample mean = 7.332 seconds and sample standard deviation = 2.073 seconds. Give your answer as a properly formatted confidence interval statement. Choose the “standard” value for C.
Solution:
Here, we have to find the confidence interval for the population mean for search time.
We are given
Sample mean = 7.332 seconds
Sample standard deviation = 2.073
Sample size = 300
Confidence level = c = 0.95
The formula for confidence interval is given as below:
X-bar -/+ t*SD/sqrt(n)
The confidence interval is given as below:
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
2.073
Sample Mean
7.332
Sample Size
300
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.119684711
Degrees of Freedom
299
t Value
1.9679
Interval Half Width
0.2355
Confidence Interval
Interval Lower Limit
7.10
Interval Upper Limit
7.57
We are 95% confident that the average population search time is lies between the two values as lower value 7.10 and upper value 7.57.
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
2.073
Sample Mean
7.332
Sample Size
300
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.119684711
Degrees of Freedom
299
t Value
1.9679
Interval Half Width
0.2355
Confidence Interval
Interval Lower Limit
7.10
Interval Upper Limit
7.57
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