Question

Major airlines compete for customers by advertising on-time arrival. A random sample of flights arriving at Toronto Pearson International Airport was obtained and the actual arrival time was compared to the scheduled arrival time. The difference (in minutes) is given in the table (a negative number indicates that the flight arrived before the scheduled arrival time).

3 -16 -1 -24 -30 23 -15 1 -2 -41 53 -26 -26 24 53 49 -13 -18 -14 17 1 8 52 -8 - 36 -25 31 -14 -4 -18 -25

d) The investigators are interested in testing whether on average the airlines arrive late. Use the data to test this claim by performing a hypothesis test at a 10% level of significance. Use a critical value to make your conclusion.

e) Construct a 90% confidence interval for the average difference in time. Interpret your interval. What does this suggest about the airline’s arrival time?

f) Did you expect your 90% confidence interval to have the same conclusion as the hypothesis test performed in part d)? Why/ Why not? (Hint: consider if this is a matching confidence interval to the hypothesis test performed in part d).)

Answer 1

we will find the mean and standard deviation of the sample first.

d)

We have no evidence to support the claim that on average the airlines arrive late.

e)

We are 90% confident that the arrival time will lie within the confidence interval calculated above.

f) This confidence interval includes 0 hence we cannot support the claim made.

This conclusion matches with the conclusion of hypothesis.