A questionnaire given to last year’s freshman class indicated that 30% intended
ID: 3255135 • Letter: A
Question
A questionnaire given to last year’s freshman class indicated that 30% intended to be science majors, 50% intended to major in the social sciences or humanities, and 20% were interested in professional programs. University officials want to determine whether there has been a change in student interests. A random sample of 100 students is surveyed from the current freshman class and the results indicate 35 students planning to major in science, 40 in the social sciences and humanities, and 25 in professional programs. Answer the following questions:
a)What are the null and alternate hypotheses?
b)What are the expected values for each of the categories?
c)What is the chi-square obtained?
d)What is the critical value?
e)What is your statistical decision? Justify your answer.
f)What is your conclusion?
Explanation / Answer
Ans: Null Hypothesis,H0: distribution of interests for both years is equally likely or have no change.
Alternate Hypothesis,Ha:distribution of interest for both years is not equally likely or have changed.
Calculated Chi square score=4.08
Degree of freedom =2
For ,degree of freedom=2 and significance level of 0.05 ,critical chi square value=5.99
As,calculated chi square score of 4.08<critical chi square value of 5.99,We fail to reject null hypothesis i.e there is no change in interests or distribution of interests is equally likely for both year.
Conclusion:There is no change in interests.
p-value approach: p-value for chi square score of 4.08 and df=2 is 0.13003
As,p-value>0.05,we fail to reject null hypothesis.
Group Observed Expected (O-E)^2/E science 35 30 0.83 social sci. 40 50 2 Prof. Prog. 25 20 1.25 100 100 4.08