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Crash Data The Insurance Institute for Highway Safety
Chapter 1, Problem 20AYU(choose chapter or problem)
Problem 20AYU
Crash Data
The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the institute’s 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver’s side. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles. The following data were collected from the institute’s study.
The researcher wants to determine if the means for head injury for each class of vehicle are different.
(a) State the null and alternative hypotheses.
(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.
(c) Test the hypothesis that the mean head injury for each vehicle type is the same at the α = 0.01 level of significance.
(d) Draw boxplots of the three vehicle types to support the analytic results obtained in part (c).
Questions & Answers
QUESTION:
Problem 20AYU
Crash Data
The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the institute’s 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver’s side. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles. The following data were collected from the institute’s study.
The researcher wants to determine if the means for head injury for each class of vehicle are different.
(a) State the null and alternative hypotheses.
(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.
(c) Test the hypothesis that the mean head injury for each vehicle type is the same at the α = 0.01 level of significance.
(d) Draw boxplots of the three vehicle types to support the analytic results obtained in part (c).
ANSWER:
Answer:
Step 1
You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles
a) We need to determine if the means for head injury for each class of vehicle are different.
The Hypotheses can be expressed as
H0 : =
H1 : At least one class has different mean for head injury.
b) The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met:
- Response variable residuals are normally distributed (or approximately normally distribution).
- Variances of populations are equal.
- Responses for a given group are independent and identically distributed normal random variables (not a simple random sample (SRS)).
The methods of one-way ANOVA are robust, so that departures from the requirement of normality will not significantly affect the results of the procedure. In addition, the requirement of equal population variances does not need to be strictly adhered to, especially if the sample size for each treatment group is the same. Therefore, it is worthwhile to design an experiment in which the samples from the populations are roughly equal in size. We can verify the requirement of normality by constructing normal probability plots by using excel.
- Start Excel.
- Open the text/data file containing the data you wish to analyze. The data should all be in one column.
- Load the Analysis Toolpak as follows:
- Under the Tools menu, choose Add-ins. From the list select Analysis Toolpak. This will allow you to perform many statistical functions within Excel.
- Create a new column of data adjacent to the original data. The new column can contain any values as long as it has the same number of entries as the original data.
- Under the Tools menu, choose Data Analysis, and then Regression. Follow the directions given in the dialog box.
- Enter values for the Input Y Range. The Input Y Range contains the data for which you want the probability plot.
- Enter values for the Input X Range. These are irrelevant in this case. We are only interested in the Normal Probability Plot option.
- Check the Normal Probability Plots option.
- Click OK
From the above plots, we see that the points on the pattern lie close to the straight line. Hence, All of the normal probability plots are roughly linear. We conclude that the sample data come from populations that are normally distributed.