UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges
ID: 3232333 • Letter: U
Question
UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding.
Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.)
test statistic and p value?
Major Women - Expected Major Women - Actual Major Art & Humanities 14.0% 670 Biological Sciences 8.4% 410 Business 13.1% 685 Education 13.0% 650 Engineering 2.6% 145 Physical Sciences 2.6% 125 Professional 18.9% 975 Social Sciences 13.0% 605 Technical 0.4% 15 Other 5.8% 300 Undecided 8.0% 420Explanation / Answer
Answer:
UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding.
Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.)
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
670
700.000
-30.000
1.286
410
420.000
-10.000
0.238
685
655.000
30.000
1.374
650
650.000
0.000
0.000
145
130.000
15.000
1.731
125
130.000
-5.000
0.192
975
945.000
30.000
0.952
605
650.000
-45.000
3.115
15
20.000
-5.000
1.250
300
290.000
10.000
0.345
420
400.000
20.000
1.000
Total
5000
4990.000
10.000
11.484
Warning: sums should be equal.
11.484
chi-square
10
df
.3211
p-value
Test statistic = 11.484
P=0.3211
Calculated P=0.3211 > 0.05 level.
We conclude that the actual college majors of graduating females fit the distribution of their expected majors.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
670
700.000
-30.000
1.286
410
420.000
-10.000
0.238
685
655.000
30.000
1.374
650
650.000
0.000
0.000
145
130.000
15.000
1.731
125
130.000
-5.000
0.192
975
945.000
30.000
0.952
605
650.000
-45.000
3.115
15
20.000
-5.000
1.250
300
290.000
10.000
0.345
420
400.000
20.000
1.000
Total
5000
4990.000
10.000
11.484
Warning: sums should be equal.
11.484
chi-square
10
df
.3211
p-value
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