Question

22. Claim: The number of car accidents is the same in Utah, Arizona and Colorado

Data: 900 crashes are chosen at random. The results are tabulated below.

? Is this evidence to refute the claim at the level of significance α = 0.05?

State Count

Utah 398

Arizona 213

Colorado 289

Total   300

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H0: The number of car accidents is the same in Utah, Arizona and Colorado.

Alternative hypothesis: Ha: The number of car accidents is not same in Utah, Arizona and Colorado.

We assume/given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

We are given

N = 3

Degrees of freedom = df = N - 1 = 3 - 1 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

State	O	E	(O - E)^2/E
Utah	398	300	32.01333333
Arizona	213	300	25.23
Colorado	289	300	0.403333333
Total	900	900	57.64666667

Test Statistic = Chi square = ∑[(O – E)^2/E] = 57.64666667

χ2 statistic = 57.64666667

P-value = 0.0000

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the number of car accidents is the same in Utah, Arizona and Colorado.

Is this evidence to refute the claim at the level of significance α = 0.05?

Answer: Yes