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	52	47	56	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:

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

1

7

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

1

7

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

1

7

H_a: All proportions are equal.

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

1

7

H_a: Not 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.)

State your conclusion:

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

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

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

D. 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?

Answer 1

a)since we expect that that proportion are equal in each of the day

option D is correct for hypothesis:

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
girls	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Sunday	1/7	66	60.00	0.77	0.600
Monday	1/7	50	60.00	-1.29	1.667
Tuesday	1/7	52	60.00	-1.03	1.067
Wednesday	1/7	47	60.00	-1.68	2.817
Thursday	1/7	56	60.00	-0.52	0.267
Friday	1/7	69	60.00	1.16	1.350
Saturday	1/7	80	60.00	2.58	6.667
total	1	420	420		14.4333
test statistic X2 =		14.433
p value =		0.0252	from excel: chidist(14.433,6)

since p value is less than significance level , we reject null hypothesis

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

category	%
Sunday	15.71%
Monday	11.90%
Tuesday	12.38%
Wednesday	11.19%
Thursday	13.33%
Friday	16.43%
Saturday	19.05%

staturday has the highest number of traffic accidents followed by Friday .