Question

# A particular report included the following table classifying 818 fatal bicycle accidents that occurred in a...

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.

Ha: p1 > 1/3, p2 < 2/3

Ha: p1 = 1/3, p2 = 2/3

Ha: p1 > 1/3, p2 > 2/3

Ha: H0 is not true.

Ha: 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.

alternative hypothesis :Ha: 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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.