Question

1. An ecologist is interested in studying the presence of different types of animal species in different locations. Using the following contingency table and the total sample size, rewrite the frequencies as relative frequencies. Round each relative frequency to two decimal places.

Location	bird species	mammal species	fish species
A	21	4	6
B	16	2	0
C	3	1	7

Location	bird species	mammal species	fish species
A
B
C

2. You are interested in learning about students' favorite mode of transportation at two universities. Fill in the blanks in the following contingency table, assuming that the variables are independent.

University	Bike	Car	Bus	Train	Other	Total
A	592	300	204		80	1202
B	410	335		20	55	1010
Total	1002	635	394	44	135	2212

3.Your teacher claims that the final grades in class are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected academic quarter, the following number of grades are recorded. Calculate the appropriate chi-square test statistic that would be used to determine if the grade distribution for the course is different than expected. Round your answer to two decimal places.

Grade	A	B	C	D	F
Number	36	42	58	10	14

4. A dog breeder wishes to see if prospective dog owners have any preference among six different breeds of dog. A sample of 200 people (prospective dog owners) provided the data below. Find the critical chi-square value that would be used to test the claim that the distribution is uniform. Use α = 0.01 and round your answer to three decimal places.

Breed	1	2	3	4	5	6
People	35	27	45	40	28	25

Answer 1

H0:  The grade distribution for the course is not different than expected

H1:  The grade distribution for the course is different than expected

Let the los be alpha = 5%

From the given data

	Observed		Expected
Grades	Freq (Oi)	Probability	Freq Ei	(Oi-Ei)^2 /Ei
A	36	0.25	40	0.4
B	42	0.25	40	0.1
C	58	0.4	64	0.5625
D	10	0.05	8	0.5
E	14	0.05	8	4.5
Total:	160	1.00	160	6.0625

Num Categories: 5
Degrees of freedom: 4

Test Statistic, X^2: 6.0625
Critical X^2: 9.48772
P-Value: 0.1945

Here P-value > alpha 0.05 and Test Statistic Chisquare value < chisquare critical value so we accept H0

thus we conclude that The grade distribution for the course is not different than expected

4) H0:  the distribution is uniform

H1:  the distribution is not uniform

From the given data

	Observed	Expected
Breed	Freq (Oi)	Freq Ei	(Oi-Ei)^2 /Ei
1	35	33.33333	0.083333333
2	27	33.33333	1.203333333
3	45	33.33333	4.083333333
4	40	33.33333	1.333333333
5	28	33.33333	0.853333333
6	25	33.33333	2.083333333
Total:	200	200	9.64

Num Categories: 6
Degrees of freedom: 5
Expected Freq: 33.33333

Test Statistic, X^2: 9.6400
Critical X^2: 11.07051
P-Value: 0.0861

Here chisquare value < chisquare critical value and P-value > alpha 0.05 so we accept H0

Thus we conclude that  the distribution is uniform