A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For51randomly selected runs, bus line A was observed to be off schedule an average time of53minutes, with standard deviation19minutes. For 61 randomly selected runs, bus line B was observed to be off schedule an average of62minutes, with standard deviation15minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.

What are we testing in this problem?

single mean

paired difference

difference of proportions

single proportion

difference of means

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀:₁=₂;H₁:₁₂

H₀:₁>₂;H₁:₁=₂

H₀:₁=₂;H₁:₁>₂

H₀:₁=₂;H₁:₁₂

What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to three decimal places.)

(c) Find (or estimate) theP-value.

P-value > 0.500

0.250 P-value

0.100 P-value

0.050 P-value

0.010 P-value

P-value

Sketch the sampling distribution and show the area corresponding to theP-value.