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 66
Monday 50
Tuesday 53
Wednesday 47
Thursday 55
Friday 69
Saturday 80
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? Use a 0.05 level of significance, what is your conclusion?
B) Compute the percentage of traffic accidents occuring on each day of the week. What day has the highest percentage of traffic accidents? Does this seem reasonable? Explain.

Answer 1

Answer:

(A) There is enough evidence to suggest that the proportion of traffic accidents is not same for each day of the week.

(B) Saturday has the highest percentage of traffic accidents.

Step-by-step explanation:

(A)

The Chi-square goodness of fit test would be used to determine if the proportion of traffic accidents is the same for each day of the week.

The hypothesis for the test can be defined as follows:

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

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

Assume that the significance level of the test is, α = 0.05.

The Chi-square test statistic is given by:

$\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}$

Compute the values in Excel.

The expected frequency for all the days is 60.

The Chi-square test statistic value is, 14.333.

Compute the p-value using the Excel function "=CHISQ.DIST.RT(14.33,6)".

p-value = 0.0262

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

The p-value is less than 0.05.

The null hypothesis will be rejected.

Conclusion:

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

(B)

Compute the percentage of traffic accidents occurring on each day of the week as follows:

$\text{Sunday}=\frac{66}{420}\times 100\approx 16\%\\\\\text{Monday}=\frac{50}{420}\times 100\approx 12\%\\\\\text{Tuesday}=\frac{53}{420}\times 100\approx 13\%\\\\\text{Wednesday}=\frac{47}{420}\times 100\approx 11\%\\\\\text{Thursday}=\frac{55}{420}\times 100\approx 13\%\\\\\text{Friday}=\frac{69}{420}\times 100\approx 16\%\\\\\text{Saturday}=\frac{80}{420}\times 100\approx 19\%$

Saturday has the highest percentage of traffic accidents.