Question

Students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Their replies are summarized below.
Degree of Certainty
credits earned very uncertain Somewhat Certain very certain Row tot
under 10 24 16 6 46
10 through 59 16 8 20 44
60 or more 2 14 22 38
col total 42 38 48 128
Under the assumption of independence, the expected frequency in the upper left cell is:__________.
A. 2.47
B. 14.56
C. 2.00
D. 11.09

Answer 1

This question is incomplete, the complete question is;

Students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Their replies are summarized below.

credits earned        very           deg.of certainty           very          Row Total

                           uncertain     somewhat certain        certain                                                

under10                    24                         16                          6                  46

10 through 59          16                           8                          20               44

60 or more               2                           14                          22               38

col total                    42                         38                         48               128

Under the assumption of independence, the expected frequency in the upper left cell is:__________.

A. 12.47

B. 14.56

C. 2.00

D. 11.09

Answer:

Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option

Step-by-step explanation:

Given the data in table in the question;

the expected frequency in the upper left cell will be;

Eij = (Ti × Tj) / N

Row total Ti = 38

Column total Tj = 42  

Total frequency N = 128

so we substitute

Eij = (38 × 42) / 128

= 1596 / 128

= 12.468 ≈ 12.47

Therefore Under the assumption of independence, the expected frequency in the upper left cell is 12.47

Option A) 12.47 is the correct Option