A bicycle safety organization claims that fatal bicycle accidents are uniformly

Question

A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table shows the day of the week in which 782 fatal bicycle accients occured. At alpha = .01, can you reject the claim that the distributuin is uniform? Complete parts a-d.

a) State Ho and Ha and identify the claim.

b) Determine the critical value and the rejection region.

c) Calculate the test statistic.

d) Decide whether to reject or fail to reject Ho. Is there enough evidence to reject the claim?

Day Frequency, f. Sunday 109 Monday 111 Tuesday 105 Wednesday 112 Thursday 121 Friday 104 Saturday 120

Explanation / Answer

A.

Ho: The distribution is uniform. [claim]
Ha: The distribution is not uniform.

B.

As

df = n - 1 = 6, at alpha = 0.01, by table or technology,

chi^2 (crit) = 16.81189383 [ANSWER]

C.

If the distirbution is uniform, then the expected value is 782/7 = 111.71 for each.

Thus, as

chi^2 = Sum[(O - E)^2/E], then

chi^2 = 2.393861893 [ANSWER]

D.

As chi^2 < chi^2 (crit), WE FAIL TO REJECT THE NULL HYPOTHESIS.

There is not enough evidence to reject the claim. [ANSWER]

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