Homework 8, Chapter 9 Solution

Problem 20: The time required for the transmission of a message
(in minutes) is sampled electronically at a communications center. The last
50 messages in the sample are as follows:

This input data is represented
as a 2 dimensional matrix to
correspond to the presentation in
the book and to make it easy to
display. It needs to be a vector

How is the transmission time distributed? Develop and test an appropriate model.

Convert data to vector

Plot the histogram

This could be a triangular or a normal distribution
Let's try comparing it to a normal distribution using a c2 test:

H0: Data are normally distributed

Since the distribution is not uniform, select intervals that
have equal probabilities.

compute the expected number of samples in each class:

Try with eight classes:

compute the expected number of samples in each class:

Try with 10 classes

compute the expected number of samples in each class:

number of cells, k c2 a=.05 for k-3 c2 result
degrees of freedom computed

Do not reject H0

Do not reject H0

Do not reject H0

Problem 21: The time (in minutes) between requests for hookup of electric service
was accurately maintained at the Gotwatts Flash and Flicker Company with the
following results for the last 50 requests:

This input data is represented
as a 2 dimensional matrix to
correspond to the presentation in
the book and to make it easy to
display. It needs to be a vector

How are the times between requests for service distributed? Develop and test
a suitable model

Convert data to vector

Plot the histogram

This looks like it could be exponentially distibuted. This would also make sense
from the source of the data.

H0: data are normally distributed

Compute c2 with 10 classes and compare it to c2 a=.05, k=8

Do not reject H0