Question

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

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 0.05 significance level, test the claim that injuries are independent of helmet color. Color of Helmet Black White Yellow Red Blue Controls (not injured) 482 350 167 90 Cases (injured or 214 113 9 44 killed) 32 70

Compute the test statistic.

Find the critical​ value(s).

What is the conclusion based on the hypothesis​ test?

Answer 1

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1.

Null hypothesis : Injuries are independent of helmet color

Alternate hypothesis: Injuries are NOT independent of helmet color

2.

The contingency table below provides the following information: the observed cell totals, (the expected cell totals) and [the chi-square statistic for each cell].

The chi-square statistic, p-value and statement of significance appear beneath the table. Blue means you're dealing with dependent variables; red, independent.

For example, for the 1st cell, it is:

O = 482

E = RowSum*ColumnSum/Total = 1121*696/1571 = 496.64

ChiSquare test statistic for 1st cell is: (O-E)^2/E = (482-496.64)^2/496.64 = 0.43

Results
	black	white	yellow	red	blue	Row Totals
control	482  (496.64)  [0.43]	350  (330.38)  [1.17]	32  (29.26)  [0.26]	167  (169.11)  [0.03]	90  (95.62)  [0.33]	1121
cases	214  (199.36)  [1.07]	113  (132.62)  [2.90]	9  (11.74)  [0.64]	70  (67.89)  [0.07]	44  (38.38)  [0.82]	450
Column Totals	696	463	41	237	134	1571  (Grand Total)

We add all cell' chi-squares and get 7.7173

Answer: The chi-square statistic is 7.7173.

Critical values are :

The p-value is .102499. The result is not significant at p < .05.

The chi-square critical statistic are: CHISQ.INV(0.025, 4) = 0.4844 and CHISQ.INV(0.975, 4) = 11.1433

Answer: Critical value(s): 0.4844, 11.1433

We fail to reject Ho as our p-value is more than .05.

Answer: Conclusion: We conclude that injuries are independent of helmet color.