Researchers are investigating the number of car crashes occurring on a certain stretch of a highway....

Researchers are investigating the number of car crashes occurring on a certain stretch of a highway. They classify the crashes as early in the week (Monday/Tuesday), mid-week (Wednesday/Thursday) or on the weekend (Friday/Saturday/Sunday). The number of crashes for each time period is given in the table below:

Early	Mid-Week	Weekend
28	34	46

Use the appropriate hypothesis test at the 5% level to determine if the proportions of crashes occurring on this stretch of highway are different for the 3 time periods.

Solutions

Expert Solution

Null hypothesis: Ho: proportions of crashes occurring on this stretch of highway are same for the 3 time periods.

Alternate hypothesis: Ha: the proportions of crashes occurring on this stretch of highway are different for the 3 time periods.

degree of freedom =categories-1=	2
for 0.05 level and 2 df :crtiical value X2 =	5.991	*from excel: chiinv(0.05,2)*
Decision rule: reject Ho if value of test statistic X2>5.991

applying chi square goodness of fit test:

	relative	observed	Expected	Chi square
Category	frequency(p)	O_i	E_i=total*p	R²_i=(O_i-E_i)²/E_i
Early	0.3333	28	36.00	1.78
Mid-Week	0.3333	34	36.00	0.11
Weekend	0.3333	46	36.00	2.78
total	1.00	108	108	4.67

test statistic X²=		4.667

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that the proportions of crashes occurring on this stretch of highway are different for the 3 time periods.

orchestra answered 1 year ago

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