Question

Each observation in a random sample of 106 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred. Data consistent with information are given in the following table. Based on these data, is it reasonable to conclude that the proportion of accidents is not the same for all days of the week? Use α = 0.05. (Round your answer to two decimal places.)

Day of Week	Frequency
Sunday	17
Monday	13
Tuesday	13
Wednesday	15
Thursday	17
Friday	18
Saturday	13

χ² =  

P-value interval

p < 0.001

0.001 ≤ p < 0.01    

0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

The proportion of accidents is  ---Select--- the same, not the same for all days.

Answer 1

We are assuming that the proportion of accidents is same on all days. Out of 106 accidents all days there will be (106/7)

Same number of accidents. Since there are 7 days we divide by seven.

Day of Week	Frequency	Expected (Ei) (106/7)
Sunday	17	15.143	0.228
Monday	13	15.143	0.303
Tuesday	13	15.143	0.303
Wednesday	15	15.143	0.001
Thursday	17	15.143	0.228
Friday	18	15.143	0.539
Saturday	13	15.143	0.303

Null Hypothesis: All days proportion of accidents is same.

Alternative: All days proportion of accidents is not same.

Test Statistic :

Test Statistic = 1.906

p - value =

df = n - 1 = 6

p - value =

= 0.928

P-value interval

p < 0.001

0.001 ≤ p < 0.01    

0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

Since p-value > 0.05

We don't reject the null hypothesis

The proportion of accidents is  the same for all days.