Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is significantly different for each type of car. Use α = 5% to hand calculate and check your work in SPSS. Compact Cars Midsize Cars Full-Size Cars

6 4 9

6 4 8

7 5 5

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.

Step-by-step explanation:

A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.

In this case we need to test whether the mean pressure applied to the driver’s head during a crash test is significantly different for each type of car.

So, a one-way ANOVA would be used.

The hypothesis can be defined as follows:

H₀: There is no difference between the means, i.e.

Hₐ: There is a significant difference between the means, i.e. at least one of the mean is different.

Use MS-Excel to perform the ANOVA test.

Go to Data – Data Analysis – Anova: Single Factor

Enter the data and enter Alpha as 0.05.

Press OK.

The output is attached below.

The F-test statistic value is, F = 5.143.

The p-value of the test is, p-value = 0.072.

Decision Rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.072 > α = 0.05

The null hypothesis will not be rejected.

Conclusion:

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.

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