# statistics

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A particular report included the following table classifying 711 fatal bicycle accidents according to time of day the accident occurred.
Time of Day Number of Accidents
Midnight to 3 a.m. 38
3 a.m. to 6 a.m. 29
6 a.m. to 9 a.m. 64
9 a.m. to Noon 78
Noon to 3 p.m. 98
3 p.m. to 6 p.m. 127
6 p.m. to 9 p.m. 164
9 p.m. to Midnight 113
(a) Assume it is reasonable to regard the 711 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 χ2 value to two decimal places, and round your P-value to three decimal places.)
χ2 =
P-value =

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 α = 0.05. Round your χ2 value to two decimal places, and round your P-value to three decimal places.)
χ2 =
P-value =

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