Question 8: In business, time is money. A local entrepreneur wants to start a regional 24/7 package delivery service for businesses along the front range. A key planning assumption is that, with Colorado Springs as the collection and distribution hub, package delivery times throughout this region will follow a Normal Probability Distribution. Using US Postal Service data and other information, an analyst constructs the following projected package delivery times (in hours) for the front range region:
1 up to 3* 4
3 up to 5 12
5 up to 7 21
7 up to 9 30
9 up to 11 25
11 up to 13 8
* Recall that "up to 3" doesn't include 3.
Given the hypotheses: H0: The package delivery time is approximately Normal**
H1: The package delivery time is not approximately Normal
** "Normal" means that the Normal Probability Distribution is followed.
a. What is the random variable for this problem.
c. Using the 0.01 level of significance and a Chi Square Goodness of Fit test, state your conclusion as to whether the package delivery times, in hours, are Normally distributed (follow the Normal pattern).
keywords: chi-squared, squared
Random variables, Expected Values, Chi-Square and Levels of Significance are investigated.