A particular report included the following table classifying 708 fatal bicycle a

Question

A particular report included the following table classifying 708 fatal bicycle accidents according to time of day the accident occurred.

(a) Assume it is reasonable to regard the 708 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.)

What can you conclude?

A) There is sufficient evidence to reject H0.

b)There is insufficient evidence to reject H0.    

(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.)

What can you conclude?

A) There is sufficient evidence to reject H0.

b)There is insufficient evidence to reject H0.    

You may need to use the appropriate table in Appendix A to answer this question.

Time of Day Number of Accidents Midnight to 3 a.m. 36 3 a.m. to 6 a.m. 29 6 a.m. to 9 a.m. 64 9 a.m. to Noon 75 Noon to 3 p.m. 99 3 p.m. to 6 p.m. 127 6 p.m. to 9 p.m. 164 9 p.m. to Midnight 114 A partislar report included the fellawing table casstiying 908 fatal bieydle accidents according to trm uf day tha ecedent occurred. Tise of Day Midright to 3 A.M Number of Accident 9 am, to Noon 164 9 *,M, to Midnight summanbid n the table a13 random ,armel. DEwtal bicycle accidents ine», rear. De these data su eette hypothean that fatal beyle accidents are not etual to constryct the tables Tast the relevare hvsotheses wsing a significance lvel af.os.(und your i' value to two deamal places, and rousd yeur P-value to thvree decmal placen.) What can yau concude? (b) Duppose a satety office poposes that bicycle fatalitias are tuice as Ibely to occur ben noon and midnight as during m dnight to roon and suppeats the followang hypathesie: Me: P: /3, s /3 whrs p th your ansier vith an aperepriate test. (Hint: Use the data te comstruct a ena-way abie ith jat tig time categariat.e 0.5 Reurd your avalus to twe decimal paces, ang round yeur vale t thros decimal places.) can ytu cenclude O There' a inaufficient Yoe may nesd to use the appropriate table in Appenda A bo anssier thia question Persanal Session Manager IN7/10

Explanation / Answer

applying chi square goodness of fit test:

2 =169.74

for (categories-1 =7) degreee of freedom and above test statsitic p value =0.000

There is sufficient evidence to reject H0.

b)

2 =6.51

p value =0.011

There is sufficient evidence to reject H0.

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E <=0.2 1/8 36.000 88.50 31.14 0.2-0.4 1/8 29.000 88.50 40.00 0.4-0.6 1/8 64.000 88.50 6.78 0.6-0.8 1/8 75.000 88.50 2.06 0.2-0.4 1/8 99.000 88.50 1.25 0.4-0.6 1/8 127.000 88.50 16.75 0.6-0.8 1/8 164.000 88.50 64.41 0.8-1.0 1/8 114.000 88.50 7.35 1 708 708 169.7401

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