Question

The table describes various degrees earned by men and women in foreign languages in 1992.

Bachelor Masters Doctorate Total

Male 3990 971 378 5339

Female 9913 1955 472 12340

Total 13903 2926 850 17679

(a) What percent of females take Doctorate degrees? (b) What percent of Masters degree holders were men? (c) Now test the null hypotheses that obtaining degrees in languages is independent of gender. Give the null and alternative hypothesis, compute the test statistic χ 2 and its degrees of freedom. (d) Is a χ 2 test appropriate for this task? (e) Use the χ 2 table to bound your P-value. What is your conclusion at α = 0.05?

Answer 1

a)  percent of females take Doctorate degrees =(472/12340)=0.0382 ~ 3.82%

b)percent of Masters degree holders were men =971/2926=0.3319 ~33.19%

c)null hypothesis:  degrees earned and gender are independent

Alternate hypothesis: Ha: degrees earned and gender are dependent

applying chi square test:

Ei=row total*column total/grand total	Bachelors	Masters	Doctors	Total
male	4198.66	883.64	256.70	5339
female	9704.34	2042.36	593.30	12340
total	13903	2926	850	17679
=(Oi-Ei)2/Ei	Bachelors	Masters	Doctors	Total
male	10.3698	8.6362	57.3219	76.328
female	4.4866	3.7365	24.8008	33.024
total	14.856	12.373	82.123	109.352

X² test statistic =109.352

degree of freedom(df) =(rows-1)*(columns-1)=

2

d)Yes as sample is random and expected frequencies are all equal or greater than 5

e)

p value <0.0001

reject HO ' sufficient evidence to conclude that degrees earned and gender are dependent