Question

Problem ONE:

The Contingency Table below shows the results of 400 randomly selected University of Toledo students to determine if there was any significant relationship between their attitude toward Donald Trump and their college major..

                                                                              Attitude Toward President Trump

Major Field                                                       Approve                             Neutral                               Dislike

Nursing/Health                                              30                                          20                          50

Liberal Arts/Social Science                       2                                            20                          68

Engineering                                                     50                                          40                          10

Business                                                            58                                          50                          2

a………If there is no relationship between one’s major and one’s attitude toward Trump, how many engineers would you expect to approve of Donald Trump?

b……..If you used a Chi-Square Test to analyze this data, how many Degrees of Freedom would this model have?

c……..True or False:

                At α = 0.01, there is a significant relationship between attitude and major field.

d……. What is the value of the Chi Square test statistic?                                                             ANSWERS

a)

b)

c)

d)

Answer 1

(a)

P(Engineering AND Approve) = 140 X 100/400 = 35

So,

Answer is:

35

(b)

Degrees of Freedom = (r - 1) X (c - 1)

                            = (4 - 1) X (3 - 1) = 6

So,

Answer is:

6

(c)

Observed Frequencies are given as follows:

Major field	Approve	Neutral	Dislike	Total
Nursing/ Health	30	20	50	100
Liberal arts/Social science	2	20	68	90
Engineering	50	40	10	100
Business	58	50	2	110
Total	140	130	130	400

The Expected Frequencies are got as follows:

Observed Frequencies are given as follows:

Major field	Approve	Neutral	Dislike	Total
Nursing/ Health	140X100/400=35	32.5	32.5	100
Liberal arts/Social science	31.5	29.25	29.25	90
Engineering	35	32.5	32.5	100
Business	38.5	35.75	35.75	110
Total	140	130	130	400

The Test Statistic got as follows:

Observed Frequency (O)	Expected frequency (E)	(O -E)2/E
30	35	0.71
20	32.5	4.81
50	32.5	9.42
2	31.5	27.63
20	29.25	2.93
68	29.25	51.34
50	35	6.43
40	32.5	1.73
10	32.5	15.58
58	38.5	9.88
50	35.75	5.68
2	35.75	31.86
Total = =		167.9876

So,

Test statistic = 167.9876

By Technology, p- value < 0.00001

Since p - value is less than = 0.01, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there is significant relationship between attitude and major field.

So,

Correct option:

True

(d)
Value of Chi square test statistic is 167.9876

Thus, answers to questions:
(a) 35

(b) 6

(c) True

(d) 167.9876