Question

In: Statistics and Probability

We anticipate that deadly two vehicle motorcycle accidents occur at the same frequency on all seven...

We anticipate that deadly two vehicle motorcycle accidents occur at the same frequency on all seven days of the week. However, is this true? The table shows the number of two-vehicle crashes including a motorbike and a passenger vehicle, with day of week, in a random sample of 1,792 accidents

Day	Freq	Relative Frequency
Sunday	329	0.18
Monday	205	0.11
Tuesday	202	0.11
Wednesday	194	0.11
Thursday	193	0.11
Friday	273	0.15
Saturday	396	0.22
Total	1792	1.0

A.What is the null and the alternative hypothesis.

B.Find the χ2 statistic and the degrees of freedom.

C.Use the critical value way to find the P-value with a significance level of α=0.05

D.What is the conclusion

Expert Solution

A.

Null Hypothesis H0: The deadly two vehicle motorcycle accidents occur at the same frequency on all seven days of the week.

Alternative Hypothesis Ha: The deadly two vehicle motorcycle accidents does not occur at the same frequency on all seven days of the week.

B.

Proportion of motorcycle accidents at any given day, p = 1/7

Expected frequency of accidents at each day, E = np = 1792 / 7 = 256

= (329 - 256)^2 / 256 + (205 - 256)^2 / 256 + (202 - 256)^2 / 256 + (194 - 256)^2 / 256 + (193 - 256)^2 / 256 + (273 - 256)^2 / 256 + (396 - 256)^2 / 256

= 150.5781

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

C.

Critical value of Chi Square statistic at α=0.05 and df = 6 is 12.59

Since observed chi square test statistic (150.5781) is greater than the critical value (12.59), P-value < 0.05

D.

We reject null hypothesis H0 and conclude that there is significant evidence that the deadly two vehicle motorcycle accidents does not occur at the same frequency on all seven days of the week.

orchestra answered 1 year ago

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