Question

27. A researcher claims that the number of motor vehicle crash deaths is consistent across age groups. The table shows the results of a random sample of motor vehicle crash deaths by age group. Are the numbers of crash deaths significantly different by age group, using a 0.05 level of significance? (15 points – Show your work!)

Age Group:	16-24	25-34	35-44	45-54	55-64	65-74	75 and older	Total
# of Crash Deaths	135	131	97	109	100	65	63	700

What are your hypotheses?

H₀:

H_A:

Fill in the following table to calculate your test statistic:

Age Group:	16-24	25-34	35-44	45-54	55-64	65-74	75 and older	Total
# of Crash Deaths	135	131	97	109	100	65	63	700
# Expected
(O – E)
(O – E)2 / E

df =______

Critical value: _________________

Conclusion: We ________ (reject / fail to reject) the Null Hypothesis

Interpretation:

Answer 1

Ho:  numbers of crash deaths are not significantly different by age group

H1:  numbers of crash deaths are significantly different by age group

Chi square test for Goodness of fit  
  
expected frequncy,E = expected proportions*total frequency = 1/7*700  
total frequency=   700

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
135	0.143	100.00	35.00		12.250
131	0.143	100.00	31.00		9.610
97	0.143	100.00	-3.00		0.090
109	0.143	100.00	9.00		0.810
100	0.143	100.00	0.00		0.000
65	0.143	100.00	-35.00		12.250
63	0.143	100	-37.00		13.690

chi square test statistic,X² = Σ(O-E)²/E =   48.700

level of significance, α=   0.05              
Degree of freedom=k-1=   7   -   1   =   6
Critical value =    12.592 [ Excel function: =chisq.inv.rt(α,df) ]      

since, test stat > critical value, reject Ho

We (reject ) the Null Hypothesis

Interpretation: we have enough evidence to conclude that numbers of crash deaths significantly different by age group