The following drawing illustrates the water-level task. Several developmental ps

Question

The following drawing illustrates the water-level task. Several developmental psychologists have investigated performance on this task. The figure on the left shows the water level in a glass of water that is half full (or is it half empty?). The figure on the right shows the same glass tipped to the right, but the water level is not shown. The task is to correctly draw the water line in this glass.

Some psychologist examined the water-level task success rate of 40 students from each of five different colleges within a university. Within each college, the sample included 20 men and 20 women. The investigators showed each participant eight different drawings of tipped glasses. If the participant correctly drew the water line on four or more of the drawings, he or she was given a "passing" result. Here is a contingency table of the results:

(a) Compare the colleges using row percentages. (Round the answers to one decimal place.)

What differences are apparent from these percentages?
The percentage passing differs among the colleges. It is lowest for students in the  ---Select--- engineering language arts social sciences business natural sciences  and highest for  ---Select--- language arts engineering natural sciences business social sciences  students.

(b) Write null and alternative hypotheses for this table.

Null hypothesis.
H0: Student's college and performance on water level task are  ---Select--- not related related  .

Alternative hypothesis.
Ha: Student's college and performance on water level task are  ---Select--- related not related  .

(c) What are the degrees of freedom, df, for a chi-square test?
df =   

(d) The chi-square statistic for this table is 14.723. Determine a p-value. (Give your answer correct to three decimal places.)
p-value =  

Result on Task College Pass Fail Total Business 27 13 40 Language Arts 23 17 40 Social Sciences 19 21 40 Natural Sciences 31 9 40 Engineering 33 7 40 Total 133 67 200 Water line is shown Draw the water line

Explanation / Answer

a)

lowest passing % - social science

highest passing % - engineering

b)

Null hypothesis.
H0: Student's college and performance on water level task are not related .

Alternative hypothesis.
Ha: Student's college and performance on water level task are related

c)

df = (r-1)(c-1) = 4

d)

p-value = 0.005311

Result on Task College Pass Fail Business 67.5 32.5 Language Arts 57.5 42.5 Social Sciences 47.5 52.5 Natural Sciences 77.5 22.5 Engineering 82.5 17.5

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