Question

Please explain how to find X2, deviations, and degrees freedom

I. Chance. (2) 1. What is the expected ratio? Table 1. Results of Tossing One Coin 50 Times Results Deviation (O-EVE Expected Deviation Heads (H) Tails (T) Total 7 c. Degrees of Freedom- d. Range of probability that deviations are due to chance- e. Accept or reject hypothesis (are the observed close enough to the expected to be due to chance?) II. Independent Events Occurring Simultaneously. a. The results of tossing two coins 50 times (2) what is the expected ratio? Results of Tossing 2 Coins 50 Times Observed Expected l. --In:L Table 2. DeviationD Deviation O-E (O-E)P/E Results H, H H, T T, T Total 2. 3. Degrees of Freedom 4. Range of probability that deviations are due to chance 5. Accept or reject hypothesis? Supplement I

Answer 1

I.

a. The result of tossing one coin 50 times.

1. The expected ratio is 1:1

Table 1.

Results	Observed	Expected	O-E	(O-E)^2	(O-E)^2/E
Heads(H)	23	25	-2	4	0.16
Tails(T)	27	25	-2	4	0.16
Total	50				0.32

b. $\chi ^{2}$= 0.32

c. Degrees of freedom = Number of E entries - 1

= 2 - 1 = 1

d. Using table of critical values for chi square distribution the range of probability that deviations are due to chance for the test statistic 0.32 and df 1 is 0.1 < p < 0.9.

e. At.0.05 level of significance we accept the hypothesis that observed are close enough to the expected to be due to the chance.

II.

a. The result of tossing two coins 50 times.

1. The expected ratio is 1:2:1

Hence, P(HH) = 1/4, P(HT) = P(TH) = =2/4, P(TT) = 1/4

Table 2

Results	Observed	Expected	O-E	(O-E)^2	(O-E)^2/E
H,H	12	12.5	-0.5	0.25	0.02
H,T	22	25	-3	9	0.36
T,T	16	12.5	3.5	12.25	0.98
Total	50				1.36

2. $\chi ^{2}$= 1.36

3. The degrees of freedom = 3-1= 2

4. Using table of critical values for chi square distribution the range of probability that deviations are due to chance for the test statistic 1.36 and df 2 is 0.1 < p < 0.9

5. At 0.05 level of significance we accept the hypothesis because 0.05 does not falls in the above range.