Question

A four-year university has decided to implement a new approach to teaching Statistics. Full-time and adjunct professors were surveyed to determine whether they preferred the traditional lecture approach or a computer approach to teaching Statistics.

status	prefers lectures	prefers computers	no preference
full time	15	13	2
adjunct	11	22	10

1. For a hypothesis test to test the independence of opinion between the two groups, identify the correct alternate hypothesis

a. H₀: The opinion is independent of status

b. H_A: The opinion is independent of status

c. H_A: The opinion is dependent upon status

d. H_A: The status is dependent upon opinion

2. For a hypothesis test to test the independence of opinion between the two groups, find the expected value (from the expected matrix) of a full-time professor who prefers lecture. i.e. E_1,1. Round to 3 decimal places.

a. 20.616

b. 10.685

c. 14.384

d. 15.315

3. For a hypothesis test to test the independence of opinion between the two groups, calculate the p-value and round to 3 significant decimal places

4. For the status versus opinion data,, for α=5%, the correct decision about H₀ is..

a. Accept H₀

b. Fail to reject H₀

c. Reject H₀

d.Fail to Accept H₀

e. Accept H_A

Answer 1

Ans:

1)Correct option is:

HA: The opinion is dependent upon status.

2)row sum=15+11=26

column sum=15+13+2=30

Overall sum=73

Expected count(full time,prefer lecture)=26*30/73=10.685

Option b is correct(10.685)

3)

	Obsered(fo)
	prefer lecture	prefer computer	no preference	Total
Full time	15	13	2	30
adjunct	11	22	10	43
Total	26	35	12	73
	Expected(fe)
	prefer lecture	prefer computer	no preference	Total
Full time	10.685	14.384	4.932	30
adjunct	15.315	20.616	7.068	43
Total	26	35		61
	Chi square=(fo-fe)^2/fe
	prefer lecture	prefer computer	no preference	Total
Full time	1.743	0.133	1.743	3.618
adjunct	1.216	0.093	1.216	2.524
Total	2.958	0.226	2.958	6.143

Test statistic:

Chi square=6.143

df=(2-1)*(3-1)=2

p-value=CHIDIST(6.143,2)=0.046

4)

As,p-value<0.05,Reject H0