Question

A particular report included the following table classifying 818 fatal bicycle accidents that occurred in a certain year according to the time of day the accident occurred.

Time of Day	Number of Accidents
midnight to 3 a.m.	47
3 a.m. to 6 a.m.	52
6 a.m. to 9 a.m.	84
9 a.m. to noon	72
noon to 3 p.m.	79
3 p.m. to 6 p.m.	157
6 p.m. to 9 p.m.	193
9 p.m. to midnight	134

For purposes of this exercise, assume that these 818 bicycle accidents are a random sample of fatal bicycle accidents.

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 data given provide evidence against this hypothesis, or are the data compatible with it? Justify your answer with an appropriate test. Use a significance level of 0.05.

State the appropriate alternative hypothesis.

H_a: p₁ > 1/3, p₂ < 2/3

H_a: p₁ = 1/3, p₂ = 2/3

H_a: p₁ > 1/3, p₂ > 2/3

H_a: H₀ is not true.

H_a: p₁ ≠ 1/3, p₂ = 2/3

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X²=

P-value=

State the conclusion in the problem context.

Reject H₀. There is convincing evidence to conclude that bicycle fatalities are not twice as likely to occur between noon and midnight as during midnight to noon.

Reject H₀. There is not convincing evidence to conclude that bicycle fatalities are not twice as likely to occur between noon and midnight as during midnight to noon.

Fail to reject H₀. There is convincing evidence to conclude that bicycle fatalities are not twice as likely to occur between noon and midnight as during midnight to noon.

Fail to reject H₀. There is not convincing evidence to conclude that bicycle fatalities are not twice as likely to occur between noon and midnight as during midnight to noon.

Answer 1

alternative hypothesis :H_a: H₀ is not true.

Applying chi square tesT:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
midnight to noon	1/3	255	272.67	-1.07	1.145
noon to midnight	2/3	563	545.33	0.76	0.572
total	1.000	818	818		1.717

X² =1.717

p value =0.1901

Fail to reject H₀. There is not convincing evidence to conclude that bicycle fatalities are not twice as likely to occur between noon and midnight as during midnight to noon.