Question

11.2.6

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 the table.

Table: Reason for Choosing a Car

Safety	Reliability	Cost	Performance	Comfort	Looks
84	62	46	34	47	27

Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level.

Answer 1

solution:

Answer Date: 06/10/2019 To test the hypothesis is that the reasons for choosing a car are equally not likely at 5% significance level. The null and alternative hypothesis is, The null hypothesis is that the reasons for choosing a car are equally likely. The alternative hypothesis is that the reasons for choosing a car are equally not likely. The chi-square test statistic for goodness-of-fit test is, First, find frequency expected then compute chi-square test statistics. The average for the observed frequencies computation is the frequencies expected. The total for the expected frequencies must equal for the total observed frequencies. The expected frequencies for category 1 are,

Total oberved frequency Expected frequency Total number of category 84 +62 +46 +34 +47 +27 6 = 50 = If the frequencies are uniformly distributed, the expected frequency is the same for each category and for other categories which are 2 to 6 each has an equal expected frequency which is 50. The chi-square test statistic for goodness-of-fit test is, x = ($o-f.)? + (46-50)2 (34 - 50) 50 50 + fe (84 – 50) – (62 – 50)? 50 50 (47-50) (27-50) + 50 50 = 42.200 +

The chi-square test statistic for goodness-of-fit test is 42.200 The chi-square critical value is, Compute degrees of freedom for finding chi-square critical values. d. f. = k-1 = 6-1 = 5 From the critical value table, show degrees of freedom 5 and the significance level 0.05, so the chi-square critical value is 11.070. The chi-square critical value is 11.070 Decision The conclusion is that chi-square test statistic 42.200 greater than chi-square critical value 11.070, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the reasons for choosing a car are equally not likely. The result is statistically significant.

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