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 63. Monday 47. Tuesday 55. Wednesday 45. Thursday 57. Friday 67. Saturday 86. 1)Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the p-value? 2. Compute the value of the x^2 test statistic (to 3 decimals). 3. The p-value =? 4. Compute the percentage of traffic accidents occuring on each day of the week (to one decimal)

Answer 1

Solution:

We are given that: a sample of 420 accidents provided the following data.

Sunday 63.

Monday 47.

Tuesday 55.

Wednesday 45.

Thursday 57. .

Friday 67.

Saturday 86.

Part 1) conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the p-value?

Step 1) State H0 and H1:

H0: the proportion of traffic accidents is the same for each day of the week.

Vs

H1: the proportion of traffic accidents is not same for each day of the week.

Step 2) Test statistic:

Where Oi = Observed frequencies

Ei = Expected Frequencies = N / k = 420 / 7 = 60

Thus we need to make following table:

Day	Oi	Ei	Oi^2/Ei
Sunday	63	60	66.150
Monday	47	60	36.817
Tuesday	55	60	50.417
Wednesday	45	60	33.750
Thursday	57	60	54.150
Friday	67	60	74.817
Saturday	86	60	123.267
	N=420

Thus Chi-square test statistic is:

Step 3) P-value:

To find exact p-value, we use Excel command:

=CHISQ.DIST.RT( x , df)

where x = and df = k - 1 = 7 - 1 = 6

=CHISQ.DIST.RT( 19.367 , 6 )

= 0.0036

Thus P-value = 0.0036

We can find P-value range by using Chi-square table:

Look in Chi-square table for df = 6 row and find the interval in which Chi-square test statistic value fall.

then find corresponding one tail area.

Chi-square test statistic value is 19.367 > 18.548

and area corresponding to 18.548 is 0.005

Thus Area corresponding to 19.367 is < 0.005

That is: P-value < 0.005

Step 4) Decision Rule:

Reject H0, if P-value < 0.05 significance level, otherwise we fail to reject H0.

Since P-value < 0.005 , that means it is also < 0.05 significance level, we reject H0.

Step 5) Conclusion:

There is not sufficient evidence to conclude that the proportion of traffic accidents is the same for each day of the week.

2. Compute the value of the x^2 test statistic

3. The p-value = 0.0036

4. Compute the percentage of traffic accidents occurring on each day of the week

We divide each Observed frequency by N = 420 and multiply by 100 to get answer in % form.

Thus we get:

Day	Oi	Percentage
Sunday	63	15.0%
Monday	47	11.2%
Tuesday	55	13.1%
Wednesday	45	10.7%
Thursday	57	13.6%
Friday	67	16.0%
Saturday	86	20.5%
	420	100.0%