Question

-10 points DevoreSts:8 14 E.008 An article focuses on the existence of any relationship between the date of patient admission for treatment of elcoholism and the patient's birthday. Assuming 365-dey year [i.e. excluding leap year), in the absence of any relation, a petient's admission date is equally likely to be any one of the 365 possible days. The investigators established four different admission categories: (1) within 7 days of birthday, [2) betreen 8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive from the birthday, and (4) more than 90 days from the birthday. A sample of 196 patients gave observed frequencies of 12, 22, 65, and 97 for catagories 1, 2, 3, and 4, respectivaly. State and test the relevant hypothezes using a significanco laval of0.01. My Notes Ask Your 46 365 at least one P-Po 184 46 120 184 ,: at least one P-Po State the rejection regian and compute the test statistic value. Round your answers to three decimal places.) rajection ragion test statistic

Answer 1

for hypothesis: last option is correct

here degree of freedom =categories-1=4-1=3

for 3 degree of freedom ; rejection region $\chi ^{2}$ >=11.345

applying chi square goodness of fit:\

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Monday	3/73	12.000	8.055		1.932
Tuesday	46/365	22.000	24.701		0.295
Wednesday	24/73	65.000	64.438		0.005
Thursday	184/365	97.000	98.805		0.033
total	1.000	196	196		2.266

test statistic $\chi ^{2}$ =2.266