Question

a. Obtain individual normal probability plots and the standard deviations of the samples.

b. Perform a residual analysis.

c. Decide whether presuming that the assumptions of normal populations and equal standard deviations are met is reasonable.

Short answer

(a) The standard deviations are

High way $3=92.9$

Gas $=126.1$

Convenience store $=139$

(b)

(c) It is acceptable to assume that the assumptions of normal populations and equal standard deviations are met.

Step-by-step solution

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

From the given data

The normal probability plot of high way

The normal probability plot of Gas station

The normal probability plot of convenience store

Use any software to find the standard deviations.

High way $3=92.9$

Gas $=126.1$

Convenience store$=139$

Part (b) Step 1: Given information

The given data is

Part (b) Step 2: Explanation

Draw the residual graph with respect to the fitted value using the given data.

The three samples have the same standard deviations as seen in the graph above. Create a normal probability map of the residuals.

Part (c) Step 1: Given information

The given data is

Part (c) Step 2: Explanation

Sections a and b

Data samples are approximately normally distributed in normal probability plots.

The residual analysis reveals that the standard deviations of all three data samples are equal.

Loss values are random and independent for three samples.

As a result, the assumptions for doing one-way ANOVA are met.

As a result, it is acceptable to assume that the assumptions of normal populations and equal standard deviations are met.