Question

A study was conducted to investigate a possible relationship between the colors of helmets worn by motorcycle drivers and whether they were injured, or not injured, in a crash. Using the results in the table below with a = 0.05, test the claim that being injured is independent of helmet color.

a) State the claim in words.

b) Write the null and alternate hypotheses. You may use symbols for the null and words for the alternate if easier.

c) Indicate which hypothesis is the claim by writing “(claim)” after the symbols.

d) Indicate if it is left-tailed, right-tailed, or two-tailed.

e) State the level of significance.

f) State the degrees of freedom.

g) List all the requirements for a contingency table.

h) Are the requirements from part g. that require calculation fulfilled?

i) Provide the formula for the test statistic

j) Compute and state the value of the test statistic.

k) Compute and state the P-value.

l) State whether you “reject H₀”or “fail to reject H₀” based on the P-value the decision rules.

m) Compute and state the critical value(s).

n) State whether you “reject H₀”or “fail to reject H₀” based on the critical value decision rules.

o) State the final conclusion for the contingency table using the appropriate words (i.e., p. 366)

	Black	White	Yellow/Orange	Red	Blue
Not Injured	491	377	31	170	55
Injured	213	112	8	70	26

Answer 1

a)Claim= Helmet color and accident are independent to each other

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b) H₀: Helmet color and accident are independent to each other

   H₁: Helmet color and accident are dependent to each other

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c) Ho ( Null hypothesis is the claim)

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d) Right tailed

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e) Level of significance = 0.05

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f) degree of freedom =(no. of rows -1)(no. of columns -1) = (2-1)(5-1) = 4

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g) The expected value of each box should be atleast 5

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h) Yes, because each value is greater than 5

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j)

Rows: C1   Columns: Worksheet columns

	Black	White	Yellow/orange	Red	Blue	All
Not Injured	491	377	31	170	55	1124
Expected count	509.53	353.92	28.23	173.70	58.62
Contribution to Chi-square	0.6737	1.5053	0.2725	0.0789	0.2241
Injured	213	112	8	70	26	429
Expected count	194.47	135.08	10.77	66.30	22.38
Contribution to Chi-square	1.7651	3.9438	0.7139	0.2068	0.5871
All	704	489	39	240	81	1553

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k) P-value = 0.041

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l) P-value < 0.05 so, Reject Ho

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m) Critical value =CHISQ.INV.RT(0.05,4)---------------Excel function

=9.488

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n) Reject Ho

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o) We have enough evidence to conclude that Helmet color and accident are dependent to each other