A human resources manager at a company based in a major city wants to determine whether there is a difference in commute times between employees who use a bus to commute to work and employees who take the subway. She surveys each employee to estimate the length of his or her daily commute. The commute times in minutes for a random sample of 10 employees who commute by bus and 10 employees who commute by subway are recorded.Assume that the population standard deviation of commute times is 5 minutes for both groups of employees and that the commute times for both groups of employees are normally distributed. Let the commute times, in minutes, by bus be the first sample, and let the commute times, in minutes, by subway be the second sample. She conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence of a difference in commute time between the two groups. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A human resources manager at a company based in a major city wants to determine whether there is a difference in commute times between employees who use a bus to commute to work and employees who take the subway. She surveys each employee to estimate the length of his or her daily commute. The commute times in minutes for a random sample of 10 employees who commute by bus and 10 employees who commute by subway are recorded.Assume that the population standard deviation of commute times is 5 minutes for both groups of employees and that the commute times for both groups of employees are
She conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence of a difference in commute time between the two groups.
(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
|
Bus Commute Time |
Subway Commute Time |
|
21 |
19 |
|
28 |
29 |
|
22 |
14 |
|
23 |
25 |
|
21 |
22 |
|
28 |
14 |
|
14 |
21 |
|
21 |
16 |
|
23 |
19 |
|
22 |
23 |
The above table shows the commute times in minutes for a random sample of 10 employees who commute by bus and 10employees who commute by subway.
(b) Use a TI-83, TI-83 Plus, or TI-84 calculator to test if the means are different. Identify the test statistic, z, and p-value from the calculator output. Round your test statistic to two decimal places and your p-value to three decimal places.
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