Question

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

Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Total
66	50	53	47	55	69	80	420

Conduct a hypothesis test to determine whether the proportion of traffic accidents is the same for each day of the week. Using a .05 level of significance, what is your conclusion?

1. Which is the correct statement of the null hypothesis?

a. H0: psun = pmon = ptue = pwed = pthu = pfri = psat is not = .143

b. H0: psun = pmon = ptue = pwed = pthu = pfri = psat is = .143

c. H0: psun not = pmon not = ptue not = pwed not = pthu not = .143

d. Ha: psun = pmon = ptue = pwed = pthu = pfri = psat is = .143

2. What is the correct statement of the null hypothesis?

a. Ha: psun = pmon = ptue = pwed = pthu = pfri = psat is not = .143

b. Ha: psun = pmon = ptue = pwed = pthu = pfri = psat is = .143

c. Ha: the population proportions are not equal to .143

d. H0: psun = pmon = ptue = pwed = pthu = pfri = psat is = .143

3. How many categories

4. What is the calculated test statistic? (4 decimals)

5. How many degrees of freedom?

6. What is the critical value? (3 decimal places)

7. What is the confident coefficient? (2 decimal places)

8. What is the alpha error? (2 decimal places)

9. What is the p-value? (4 decimal places)

10. What is the conclusion?

a. reject the null hypothesis all proportions of accidents are not different

b. do not reject the null hypothesis the proportions of accidents are different

c. do not reject the null hypothesis all proportions of accidents are not different

d. reject the null hypothesis some of the proportions of accidents are different

Answer 1

1. Which is the correct statement of the null hypothesis?

Expected proportion of traffic accidents on each day = 1/7 = 0.143

Thus the correct statement of the null hypothesis is,

b. H0: psun = pmon = ptue = pwed = pthu = pfri = psat is = .143

2. What is the correct statement of the alternate hypothesis?

The correct statement of the alternate hypothesis is,

c. Ha: the population proportions are not equal to .143

3. How many categories

There are 7 categories (7 days of the week)

4. What is the calculated test statistic? (4 decimals)

Expected number of accidents on any day = 0.143 * 420 = 60

Chi-square test statistic, = (Oi - Ei)² / Ei where Oi and Ei is the observed and expected proportion of accidents.

= (66 - 60)² /60 + (50 - 60)² /60 + (53 - 60)² /60 + (47 - 60)² /60 + (55 - 60)² /60 + (69 - 60)² /60 + (80 - 60)² /60

= 14.33333

5. How many degrees of freedom?

Degree of freedom = Number of categories - 1 = 7 - 1 = 6

6. What is the critical value? (3 decimal places)

Critical value of Chi-square test statistic at .05 level of significance is 12.59

7. What is the confident coefficient? (2 decimal places)

confident coefficient = 1 - significance level = 1 - 0.05 = 0.95

8. What is the alpha error? (2 decimal places)

alpha error = significance level = 0.05

9. What is the p-value? (4 decimal places)

p-value = P( > 14.33, df = 6) = 0.026

10. What is the conclusion?

Since p-value is less than the 0.05 significance level,

d. reject the null hypothesis some of the proportions of accidents are different