Question

Day 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 775 randomly selected fatal bicycle accidents occurred. At a = 0.10, can you reject the claim that the distribution is uniform? Complete parts a through d below. Frequency, f 109 111 105 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 120 106 112 (a) State Ho and H, and identify the claim. Ho: The distribution of fatal bicycle accidents throughout the week is Hy: The distribution of fatal bicycle accidents throughout the week is Which hypothesis is the claim? оно она (b) Determine the critical value, Xo, and the rejection region. Xo = (Round to three decimal places as needed.) Choose the correct rejection region below. O A. x² >x OC. x <x2 OB. x??X? OD. x sx (c) Calculate the test statistic. x? -(Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. V Ho. At the 10% significance level, there Venough evidence to reject the claim that the distribution of fatal bicycle accidents thoughout the week is uniform.

Answer 1

Answer:

To test,

a)

Ho: The distribution of fatal bicycle accidents throughout the week is uniformly distributed. ( Claim)

H1:The distribution of fatal bicycle accidents throughout the week is not uniformly distributed.

b)

Use $\alpha =0.10$

d.f= K-1=7-1=6

The critical value for chi-square test :

$\chi _{0}^{2}=10.645$ ( From Chi-square table)

The rejection region is $\chi ^2>\chi _{0}^{2}$

c)

Day	frequency(O)	Expected(E)	(oi-Ei)	(oi-Ei)^2	(Oi-Ei)^2/Ei
Sunday	109	110.714	-1.714	2.937796	0.026535
Monday	111	110.714	0.286	0.081796	0.000739
Tuesday	105	110.714	-5.714	32.6498	0.294902
Wednesday	112	110.714	1.286	1.653796	0.014938
Thursday	120	110.714	9.286	86.2298	0.778852
Friday	106	110.714	-4.714	22.2218	0.200714
Saturday	112	110.714	1.286	1.653796	0.014938
Total	N=775				1.331616
# Expected count=775/7	110.714

Test statistic($\chi ^2$)=1.332

Where, $\chi ^2$ _calculated <  $\chi ^2$_tabulated

We accept Ho.

Conclusion: At the 10% significance level, there is not enough evidence to reject the claim that the distribution of fatal bicycle accidents throughout the week is uniformly distributed.