Question

#2: Here is a contingency (frequency) table based on some recent data. CSUDH students majoring in psychology or business were ask which option they’d choose given the choice between taking intermediate statistics and receiving one semester’s credit for participation in a local dental school’s study of a new root canal procedure done entirely without anesthesia.

CHOICE                     STATISTICS ROOT CANAL

MAJOR

PSYCHOLOGY                     35                                55                               

BUSINESS                            70                               25                               

                                               

ANSWER THE FOLLOWING QUESTIONS:

A. What is the ratio of psychology to business majors?           

B. What proportion and percentage of the sample were business majors?         

C. At the .05 level test to see if there is an association between major and preference for statistics or root canal.

Answer 1

Result:

Here is a contingency (frequency) table based on some recent data. CSUDH students majoring in psychology or business were ask which option they’d choose given the choice between taking intermediate statistics and receiving one semester’s credit for participation in a local dental school’s study of a new root canal procedure done entirely without anesthesia.

CHOICE                     STATISTICS ROOT CANAL

MAJOR

PSYCHOLOGY                     35                                55                               

BUSINESS                            70                               25                               

                                               

ANSWER THE FOLLOWING QUESTIONS:

A. What is the ratio of psychology to business majors?           

The ratio is 90: 95    OR 18: 19

B. What proportion and percentage of the sample were business majors?         

Proportion = 95/185 = 0.5135

OR

Percentage= 51.35%

C. At the .05 level test to see if there is an association between major and preference for statistics or root canal.

Ho: there is no association between major and preference for statistics or root canal.

H1: there is an association between major and preference for statistics or root canal.

Chi-Square Test
Observed Frequencies
	Column variable				Calculations
Row variable	STATISTICS	ROOT CANAL	Total		fo-fe
PSYCHOLOGY	35	55	90		-16.0811	16.0811
BUSINESS	70	25	95		16.0811	-16.0811
Total	105	80	185
Expected Frequencies
	Column variable
Row variable	STATISTICS	ROOT CANAL	Total		(fo-fe)^2/fe
PSYCHOLOGY	51.0811	38.9189	90		5.0626	6.6446
BUSINESS	53.9189	41.0811	95		4.7961	6.2949
Total	105	80	185
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	2
Degrees of Freedom	1
Results
Critical Value	3.8415
Chi-Square Test Statistic	22.7982
p-Value	0.0000
Reject the null hypothesis

DF=1

Chi square value at 0.05 level =3.841

Calculated chi square =22.798 > 3.841 the table value.

The null hypothesis is rejected.

At the 5% level of significance, we conclude that there is significant association between major and preference for statistics or root canal.