Question

The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data.

Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
66	50	53	48	54	69	80

(a)

Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. Use a 0.05 level of significance.

State the null and alternative hypotheses.

H₀: p_Sun = p_Mon = p_Tue = p_Wed = p_Thu = p_Fri = p_Sat =

1

7

H_a: Not all proportions are equal.H₀: Not all proportions are equal.
H_a: p_Sun ≠ p_Mon ≠ p_Tue ≠ p_Wed ≠ p_Thu ≠ p_Fri ≠ p_Sat ≠

1

7

    H₀: Not all proportions are equal.
H_a: p_Sun = p_Mon = p_Tue = p_Wed = p_Thu = p_Fri = p_Sat =

1

7

H₀: p_Sun ≠ p_Mon ≠ p_Tue ≠ p_Wed ≠ p_Thu ≠ p_Fri ≠ p_Sat ≠

1

7

H_a: All proportions are equal.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We conclude that the proportion of traffic accidents is not the same for each day of the week.Do not reject H₀. We conclude that the proportion of traffic accidents is the same for each day of the week.     Do not reject H₀. We conclude that the proportion of traffic accidents is not the same for each day of the week.Reject H₀. We conclude that the proportion of traffic accidents is the same for each day of the week.

(b)

Compute the percentage of traffic accidents occurring on each day of the week. (Round your answers to two decimal places.)

Sunday %Monday %Tuesday %Wednesday %Thursday %Friday %Saturday %

What day has the highest percentage of traffic accidents?

SundayMonday    TuesdayWednesdayThursdayFridaySaturday

Answer 1

a) H₀: p_Sun = p_Mon = p_Tue = p_Wed = p_Thu = p_Fri = p_Sat = 1/7

H_a: Not all proportions are equal

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Sun	1/7	66	60.000	0.77	0.600
Mon	1/7	50	60.000	-1.29	1.667
Tue	1/7	53	60.000	-0.90	0.817
Wed	1/7	48	60.000	-1.55	2.400
Thu	1/7	54	60.000	-0.77	0.600
Fri	1/7	69	60.000	1.16	1.350
Sat	1/7	80	60.000	2.58	6.667
total	1.000	420	420		14.1000
test statistic X2 =		14.100

p value =

0.0285

Reject H₀. We conclude that the proportion of traffic accidents is not the same for each day of the week.

category	%
Sun	15.71%
Mon	11.90%
Tue	12.62%
Wed	11.43%
Thu	12.86%
Fri	16.43%
Sat	19.05%

highest percentage of traffic accidents is on Saturday