A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed througho

Lubna Boyce

Lubna Boyce

Answered question

2022-03-03

A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table on the right shows the day of the week for which 777 randomly selected fatal bicycle accidents occurred. At α=0.01, can you Frequency, f Day Sunday Monday Tuesday Wednesday Thursday reject the claim that the distribution is uniform? Complete parts a through d below.
 Day  Frequency, f  Sunday 107 Monday 113 Tuesday 105 Wednesday 110 Thursday 122 Friday 104 Saturday 116
Which hypothesis is the claim?
a. H0
b. Ha
Determine the critical value, χ02 and the rejection region

Answer & Explanation

surgescasjag

surgescasjag

Beginner2022-03-04Added 10 answers

Applying Chi-square test,
Expected frequency (E)=Total/n=777/7=111
Chi-square test statistic (χ2):
 Day  Observed  Expected frequency (E)  (O-E)^2  (O-E)^2/E  Sunday 107111160.1441 Monday 11311140.0360 Tuesday 105111360.3243 Wednesday 11011110.0090 Thursday 1221111211.0901 Friday 104111490.4414 Saturday 116111250.2252 Che-square test statistic (χ2)=2.2703
Chi-square test statistic (χ2)=(OE)2E=2.2703
degree of freddom (df)=n-1=7-1=6
α=0.01
The test statistic follows the χ2-distribution with 6 degrees of freedom.
χ2 critical = 16.812 (by using excel)
Decision criteria: Reject Ho,if Chi-square test statistic (χ2)>χ2 critical.
Since,Chi-square test statistic (χ2)<χ2 critical, we fail to reject the null hypothesis.

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