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A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars.

A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars.: Expert Solutions for Success

A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in table F.

Table #F: Reason for Choosing a Car

Safety	Reliability	Cost	Performance	Comfort	Looks
80	65	56	33	49	37

Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 10% level.

Answer

The hypotheses are:

Null hypothesis Ho: the reasons for choosing a care are equaly likely.

Alternative hypothesis Ha: the reasons for choosing a car are not equally likely.

	Safety	Reliability	Cost	Performance	Comfort	Looks	Total	Expected Frequency
	80	65	56	33	49	37	320	53.333
x²	13.334	2.552	0.133	7.752	0.352	5.002	29.125

The chi-square test statistic is 29.125

To get chi-square critical value is, we need to find the degrees of freedom for finding the chi-square critical values,

df= 6-1 =5

From the critical value chi-square table, the significance level is 0.1 for df= 5 and the chi-square critical value = 9.236

Conclusion

Chi-square test statistic for goodness-of-fit test 29.125 is greater than chi-square critical value 9.236; therefore, we reject the null hypothesis at 10% significance level. Thus, there is a significant evidence to indicate that the reasons for choosing a car are not equally likely.

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