Question

A new advertising program involves placing small screens on the back of taxi front seats in order to run several advertisements continuously. The theory is that riders give their undivided attention to these ads during the entire trip. To understand the potential of the advertising program, advertisers would like to first learn about the length of time of taxi rides. Random samples of the taxi ride times (in minutes) in two cities were obtained. Please assume that the distributions are normal. The summary data are given in the following table. You will not need to use the information from all the rows. Please provide three decimal places for all answers. All critical values should have four decimal places.

Length of Taxi Ride (minutes)	n	x̄	s
San Diego	24	20.322	6.191
Phoenix	24	15.07	5.773
San Diego - Phoenix	24	5.252	8.106

Is there any evidence to suggest the true mean lengths of the taxi rides are different in the two cities? Use α= 0.01.

a. (0.5 pts.)Calculate the test statistic. Be sure that the information for San Diego is first and the information for Phoenix is second.

b. (0.5 pts.) Calculate the p-value.

c) Calculate the 99% confidence interval for the mean. The critical value is from the table in the book.

d) In practical terms, does the data imply that the true lengths of taxi rides are different in the two cities? Please explain your reasoning. This part uses the information from parts b) and c). However, if your explanation only involves inferential statistics, you will receive 0 points.

Answer 1

The hypothesis are

H0: v/s H1:

a) The test statistic is

Where,

= 5.986

= 3.039

b) p value =2* p ( t < 3.039 )

Use excel formula " = t.dist.2T (x,df) " , "=t.dist.2T(3.039,46)"

So p value = 0.0039

Here p value < ( 0.01 ) . Hence we reject null hypothesis.

Conclusion : There is evidence to suggest the true mean lengths of the taxi rides are different in the two cities.

c) The 99% confidence interval is given by

{ ( ​ ) - E , ( ​ ) + E }

Where,

c = 0.99, df = 24 +24 - 2 = 46 ,

tc =

( using excel formula "=t.inv.2t(probability,df) " ="t.inv.2t(0.01, 46 ) " )

Hence,

= 4.643

Hence the required confidence interval is given by,

{ ( 20.322 - 15.07 ) - 4.643 , ( 20.322 - 15.07 ) + 4.643 }  

( 0.609, 9.895 )

d) In part B, as null hypothesis is rejected, we conclude that the data imply that the true lengths of taxi rides are different in the two cities.  

In part C, here null hypothesis value for difference in two population means is 0.

( H0 : i.e. H0 : )

The confidence interval do not contain null hypothesis value 0, hence we reject null hypothesis. So we conclude that the data imply that the true lengths of taxi rides are different in the two cities.