Question

The table below shows the distribution of the opinions of US parents as to whether a college education is worth the expense:

STRONGLY AGREE	SOMEWHAT AGREE	NEITHER AGREE NOR DISAGREE	SOMEWHAT DISAGREE	STRONGLY DISAGREE
55%	30%	5%	6%	4%

An economist claims that the distribution of the opinions of US teenagers on this question is different from the distribution of the opinions of US parents. To test this claim, you randomly survey 200 US teenagers, and the results are:

STRONGLY AGREE	SOMEWHAT AGREE	NEITHER AGREE NOR DISAGREE	SOMEWHAT AGREE	STRONGLY AGREE
86	62	34	14	4

Test the economist’s claim.

A.) What are the hypotheses?

B.) What is the value of the test statistic?

C.)What is the p-value?

D.)What is the result of this hypothesis test in terms of rejecting or failing to reject the null hypothesis?

E.) What can we conclude from the hypothesis test?

Answer 1

A) ho: distribution of the opinions of US parents as to whether a college education is worth the expense is: p1=55%; p2=30%, p3=5%, p4=6%, p5=4%

H1: at least one of the proportion in the distribution of the opinion of us playing as to whether a college education is work experience defer significantly. At least one, p1=/=55%; p2=/=30%, p3=/=5%, p4=/=6%, p5=/=4%

B)

	Oi	Pi	Ei = pi*N	(Oi-ei)^2/Ei
	86	0.55	110	5.24
	62	0.3	60	0.07
	34	0.05	10	57.60
	14	0.06	12	0.33
	4	0.04	8	2.00
SUM	200	1.0000	200	65.24

Chisq= 65.236 = sum(Oi-Ei)^2/Ei

C) p-value= 2.29445E-13 = CHISQ.TEST(B2:B4,D2:D4)

D) since the P-value is less than Alpha, 5%, the null hypothesis is rejected at 5% level of significance.

E) at least one of the proportion in the distribution of the opinion of us playing as to whether a college education is work experience defer significantly. At least one, p1=/=55%; p2=/=30%, p3=/=5%, p4=/=6%, p5=/=4%