Question
A transportation agency would like to compare the average amount of time it takes passengers to pass through airport security at two locations during peak
A transportation agency would like to compare the average amount of time it takes passengers to pass through airport security at two locations during peak times. The following table summarizes in minutes the results of two random samples from each airport. Use the table to complete parts a through c.
Location 1 | Location 2 | |||
Sample mean | 14.6 | 11.9 | ||
Sample standard deviation | 5.9 | 4.8 | ||
Sample size | 23 | 29 |
a. Perform a hypothesis test using
=0.05
to determine if the average time to pass through security in location 1 is more than the average time to pass through security in location 2. Assume the population variances for time through security at these two locations are equal.
Determine the null and alternative hypotheses for the test.
H0:12
less than or equals
0
H1:12
greater than>
0
Calculate the appropriate test statistic and interpret the result.
The test statistic =
enter your response here.
(Round to two decimal places as needed.
The critical value(s) is(are)
(Round to two decimal places as needed. Use a comma to separate answers as needed.
Because the test statistic
is ................... , ...............................
the null hypothesis.
b. Identify the p-value from part a and interpret the result.
The p-value is
(Round to three decimal places as needed.
Interpret the result. Choose the correct answer below.
A.
Since the p-value is
notless
than the significance level,
donotreject
the null hypothesis.
Your answer is not correct.
B.
Since the p-value is
notless
than the significance level,
reject
the null hypothesis.
C.
Since the p-value is
less
than the significance level,
donotreject
the null hypothesis.
D.
Since the p-value is
less
than the significance level,
reject
the null hypothesis.
This is the correct answer.
c. What assumptions need to be made in order to perform this procedure?
A.
Although the sample size in the second sample is large enough, it must be assumed that the distribution for the first sample is normally distributed, and that the samples are independent.
B.
Since the sample sizes are large enough, no assumptions are needed.
C.
It must be assumed that the distribution for both populations are normally distributed, and that the samples are independent.
D.
Although the sample size in the first sample is large enough, it must be assumed that the distribution for the second population is normally distributed, and that the samples are independent
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