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. For 51 randomly selected runs,
bus line A was observed to be off schedule an average time of 53
minutes, with standard deviation 19minutes. For 61 randomly
selected runs, bus line B was observed to be off schedule an
average of 62 minutes, with standard deviation 15 minutes. 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 meanpaired difference difference of proportionssingle proportiondifference of means
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 > μ2; H1: μ1 = μ2 H0: μ1 = μ2; H1: μ1 > μ2H0: μ1 = μ2; H1: μ1 < μ2
(b) What sampling distribution will you use? What assumptions are
you making?
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? (Test the
difference μ1 − μ2. Round
your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010
Sketch the sampling distribution and show the area corresponding to
the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level α?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the
application.
There is sufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.
difference of means
A)
level of significance =0.05
H0: μ1 = μ2; H1: μ1 ≠ μ2
b)
the student t . We assume that both population distributions are approximately normal with unknown standard deviations |
std error of difference= | √(S21/n1+S22/n2) | = | 3.281 | ||
test stat t = | (x1-x2-Δo)/Se | = | -2.743 |
c)P-value < 0.010
bottom left plot is correct
d)(
at the 0.05 level, we reject the null hypothesis and conclude the data are statistically significant |
e)There is insufficient evidence at the 0.05 to conclude that there is a difference in average off schedule times.
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