Question

A​ case-control (or​ retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance​ level, test the claim that injuries are independent of helmet color.

	black	white	yellow	red	blue
controls(not injured)	487	360	34	158	78
cases (injured or killed)	209	104	9	66	38

1)Identify the null and alternative hypotheses. Choose the correct answer below.

2)Compute the test statistic.​(Round to three decimal places as​ needed.)

3)Find the critical​ value(s)​(Round to three decimal places as needed)

4)What is the conclusion based on the hypothesis​ test?

Answer 1

Answer:

1) Hypotheses:

Null Hypothesis (H0): The injuries are independent of helmet color

Alternate Hypothesis (H1): The injuries are dependent of helmet color

2)

Chi-square test-static:

Test Static = 11.190

3) Critical Values:

alpha = 0.01, df = 4

critical value = 13.277

4) chi square test static = 11.190 < 13.277

We failed to reject the null hypothesis

at 1% significance level, we conclude that there is sufficient evidence that the injuries are dependent of helmet color