Question

Use the following information to answer the questions. A more recent study of Feline High-Rise Syndrome (FHRS) included data on the month in which each of 119 cats fell ( Vnuk et al. 2004) The data are in the accompanying table. Can we infer that the rate of cat falling varies between months of the year?

Month Number fallen

January 4

February 6

March 8

April 10

May 9

June 14

July 19

August 13

September 12

October 12

November 7

December 5

1. Assume a catfall is equally likely to occur in each month and carry out a suitable test.

2. Assume a catfall is equally likely to occur on each day and carry out a suitable test. Use a calendar for a non-leap year to obtain the needed probabilities.

3. Which method out of (a) and (b) would be best to use, if it were reasonable to assume that a cat could fall at any moment? Explain, briefly.

Answer 1

a) Here we define

Null Hypothesis: Rate of cat falling does not varies between months of the year

Alternate Hypothesis : Rate of cat falling varies between months of the year

at 5% level of significance we use the chi square statistics

Months	Number of cat falling	Expected no of cat falling
	Observed (1)	Expected (2)	O-E (3)	(O-E)^2 (4)	(4) /(2)
Jan	4	9.92	-5.92	35.01	3.53
Feb	6	9.92	-3.92	15.34	1.55
Mar	8	9.92	-1.92	3.67	0.37
Apr	10	9.92	0.08	0.01	0.00
May	9	9.92	-0.92	0.84	0.08
Jun	14	9.92	4.08	16.67	1.68
Jul	19	9.92	9.08	82.51	8.32
Aug	13	9.92	3.08	9.51	0.96
Sep	12	9.92	2.08	4.34	0.44
Oct	12	9.92	2.08	4.34	0.44
Nov	7	9.92	-2.92	8.51	0.86
Dec	5	9.92	-4.92	24.17	2.44
Total	119				20.6639

at 5 % level of significance the tabulated value of Chi Square is 19.7 at 11 degree of freedom

since calculated value of chi square ( 20.66) is greater than tabulated value ( 19.7)

Therefore Null Hypothesis is rejected and we conclude that rate of cat falling varies between the months

b)  

Null Hypothesis: Rate of cat falling does not varies between days of the year

Alternate Hypothesis : Rate of cat falling varies between Days of the year

at 5% level of significance we use the chi square statistics

Months	Number of cat falling	Number of days	Cat fallen per day
	Observed (1)		observed	expected	O-E	(O-E)^2	(O-E)^2 /E
Jan	4	31	0.13	0.33	-0.20	0.040	0.122
Feb	6	28	0.21	0.33	-0.12	0.013	0.041
Mar	8	31	0.26	0.33	-0.07	0.005	0.016
Apr	10	30	0.33	0.33	0.00	0.000	0.000
May	9	31	0.29	0.33	-0.04	0.002	0.005
Jun	14	30	0.47	0.33	0.14	0.019	0.057
Jul	19	31	0.61	0.33	0.28	0.080	0.243
Aug	13	31	0.42	0.33	0.09	0.008	0.024
Sep	12	30	0.40	0.33	0.07	0.005	0.015
Oct	12	31	0.39	0.33	0.06	0.003	0.010
Nov	7	30	0.23	0.33	-0.10	0.009	0.028
Dec	5	31	0.16	0.33	-0.17	0.028	0.086
Total	119	365					0.646
	Expected	365/119

here for 365-1 = 364 degree of freedom the calculated value of chi square is 0.646 which is very much less than the tabulated value

therefore, we do not reject the null hypothesis and conclude that rate of cat falling does not varies between days

c) the method on the basis of days is better to chose to assume the cat can fall at any moment as it is independent if days and so of moment.

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