A particular report included the following table classifying 709 fatal bicycle a

Question

A particular report included the following table classifying 709 fatal bicycle accidents according to time of day the accident occurred.

(a) Assume it is reasonable to regard the 709 bicycle accidents summarized in the table as a random sample of fatal bicycle accidents in that year. Do these data support the hypothesis that fatal bicycle accidents are not equally likely to occur in each of the 3-hour time periods used to construct the table? Test the relevant hypotheses using a significance level of .05. (Round your 2 value to two decimal places, and round your P-value to three decimal places.)

(b) Suppose a safety office proposes that bicycle fatalities are twice as likely to occur between noon and midnight as during midnight to noon and suggests the following hypothesis: H0: p1 = 1/3, p2 = 2/3, where p1 is the proportion of accidents occurring between midnight and noon and p2 is the proportion occurring between noon and midnight. Do the given data provide evidence against this hypothesis, or are the data consistent with it? Justify your answer with an appropriate test. (Hint: Use the data to construct a one-way table with just two time categories. Use = 0.05. Round your 2 value to two decimal places, and round your P-value to three decimal places.)

Time of Day Number of Accidents Midnight to 3 a.m. 36 3 a.m. to 6 a.m. 28 6 a.m. to 9 a.m. 64 9 a.m. to Noon 77 Noon to 3 p.m. 98 3 p.m. to 6 p.m. 127 6 p.m. to 9 p.m. 165 9 p.m. to Midnight 114

Explanation / Answer

Ans:

a)

df=8-1=7

As,p-value<0.05,we reject null hypothesis.

There is sufficient evidence to support that fatal bicycle accidents are not equally likely to occur in each of the 3-hour time periods

b)

df=2-1=1

As,p-value<0.05,we reject null hypothesis.

There is not sufficient evidence to support that given data have specified distribution(i.e p1=1/3,p2=2./3)

or we can conclude that given data is not consistent with the specified distribution.

Time of Day Number of Accidents(O) Expected(E) (O-E)^2/E Midnight to 3 a.m. 36 88.625 31.25 3 a.m. to 6 a.m. 28 88.625 41.47 6 a.m. to 9 a.m. 64 88.625 6.84 9 a.m. to Noon 77 88.625 1.52 Noon to 3 p.m. 98 88.625 0.99 3 p.m. to 6 p.m. 127 88.625 16.62 6 p.m. to 9 p.m. 165 88.625 65.82 9 p.m. to Midnight 114 88.625 7.27 Total= 709 709 171.78

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