There are three different ways I can go to work in the morning. I want to see if there is a difference in the distributions of travel-times between the three different ways. The sample data is depicted below. I claim there is a difference in mean travel times between the three different routes. I cannot guarantee that the distributions of these travel times are Normal. Travel Time in Minutes Interstate 22 22 21 23 22 21 Route 15 22 18 20 18 Back Roads 19 19 18 19 22 (a) Enter the rank values in the same order as in the original sample. Interstate Route 15 Back Roads (b) Give the value of the test statistic: (c) Test my claim at the 10% significance level. Enter the critical value: There is sufficient evidence to conclude that the population means are not equal. Yes No (d) Does your conclusion change at the 5% significance level? Yes No
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.
There are three different ways I can go to work in the morning. I want to see if there is a difference in the distributions of travel-times between the three different ways. The sample data is depicted below. I claim there is a difference in mean travel times between the three different routes. I cannot guarantee that the distributions of these travel times are Normal.
| Travel Time in Minutes | ||||||
| Interstate | 22 | 22 | 21 | 23 | 22 | 21 |
| Route 15 | 22 | 18 | 20 | 18 | ||
| Back Roads | 19 | 19 | 18 | 19 | 22 |
(a) Enter the rank values in the same order as in the original sample.
| Interstate | ||||||
| Route 15 | ||||||
| Back Roads |
(b) Give the value of the test statistic:
(c) Test my claim at the 10% significance level.
Enter the critical value:
There is sufficient evidence to conclude that the population means are not equal.
Yes
No
(d) Does your conclusion change at the 5% significance level?
Yes
No
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