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 |
|---|---|---|---|---|---|---|
| 69 | 47 | 54 | 49 | 58 | 69 | 74 |
a. 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?
Compute the value of the X2 test statistic (to 3 decimals).
_____
The -value is - Select your answer -between .01 and .025,between .025 and .05,between .05 and .10,greater than .10,less than .01.
Using a .05 level of significance, what is your conclusion?
- Select your answer: Conclude -OR- Cannot conclude the proportion of traffic accidents is not the same for each day of the week.
b. Compute the percentage of traffic accidents occurring on each day of the week (to 1 decimal).
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | |
|---|---|---|---|---|---|---|---|
| Percentage of traffic accidents, |
What day has the highest percentage of traffic accidents?
- Select your answer -MondayTuesdayWednesdayThursdayFridaySaturdaySundayItem 11
Does this seem reasonable? Discuss.
- Select your answer -Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday has the highest number of accidents, followed by - Select your answer -MondayTuesdayWednesdayThursdayFridaySaturday. This makes sense because these are times when people go out and may be consuming alcohol, having distractions such as more people in their car, and speeding.
a)
Chi square test for Goodness of fit
expected frequncy,E = expected proportions*total
frequency
total frequency= 420
| observed frequencey, O | expected proportion | expected frequency,E | (O-E)²/E | ||
| 69 | 0.143 | 60.00 | 1.350 | ||
| 47 | 0.143 | 60.00 | 2.817 | ||
| 54 | 0.143 | 60.00 | 0.600 | ||
| 49 | 0.143 | 60.00 | 2.017 | ||
| 58 | 0.143 | 60.00 | 0.067 | ||
| 69 | 0.143 | 60.00 | 1.350 | ||
| 74 | 0.143 | 60 | 3.267 |
chi square test statistic,X² = Σ(O-E)²/E =
11.467
level of significance, α= 0.05
Degree of freedom=k-1= 7 -
1 = 6
p value = between .05 and .10
Decision: P value >α , Do not reject Ho
Cannot conclude the proportion of traffic accidents is not the same for each day of the week
b)
| category | percentage | |||
| sun | 16.4% | |||
| mon | 11.2% | |||
| tue | 12.9% | |||
| wed | 11.7% | |||
| thu | 13.8% | |||
| fri | 16.4% | |||
| sat | 17.6% |
Saturday has the highest percentage of traffic accidents (17.6%)
This makes sense because these are times when people go out and may be consuming alcohol, having distractions such as more people in their car, and speeding.
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