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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 |
|
|
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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