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 work and answers unless explicity mentioned otherwise.

Length of Taxi Ride (minutes)	n	x̄	s
San Diego	28	20.32	6.191
Phoenix	28	15.39	5.773
San Diego - Phoenix	28	4.93	8.119

a) Should this situation be analyzed via a two-sample independent or two-sample paired method? Note that you will only get one try to get this question correct.Please explain the correct answer. If this is a paired situation, please state the common characteristic that makes these data paired.

b) What is the alternative hypothesis for this situation?Please explain the correct answer.

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

i) Calculate the test statistic. Be sure that the information for San Diego is first and the information for Phoenix is second.

ii) Calculate the p-value. Please submit 4 decimal places.

iii) Write the complete four steps of the hypothesis test below.

iv) Please show all of the code for part c) below.

d) Calculate the 99% confidence interval or bound for the mean. If you are calculating a bound, type 10000 to indicate ∞.

e) Interpret the interval or bound calculated above. In addition to the interpretation, please state the critical value.

f) Please show all of the code for part d) below.

g) 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 c) and d). However, if your explanation only involves inferential statistics, you will receive 0 points.

h) What would change in this analysis if the cities were reversed; that is, we used Phoenix – San Diego instead of San Diego - Phoenix? Would the conclusion change? Please explain your answer.

Answer 1

g) 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 c) and d). However, if your explanation only involves inferential statistics, you will receive 0 points.

Ans: The p-value inc) is 0.0032 and less than 0.01 level of significance. Also, the 99% CI in d) does not include the value zero. Hence, we can conclude that in practice, the data imply that the true lengths of taxi rides are different in the two cities at 0.01 level of significance.

h) What would change in this analysis if the cities were reversed; that is, we used Phoenix – San Diego instead of San Diego - Phoenix? Would the conclusion change? Please explain your answer.

Ans: If a change in this analysis if the cities were reversed; that is, we used Phoenix – San Diego instead of San Diego - Phoenix, we will not change the conclusion but the 99% CI will have negative sign on both the upper and lower limits.