Question

From research, it is known that the opinions of US parents on whether a college education is worth the expense is the following: strongly agree 55%, somewhat agree 30%, neither agree nor disagree 5%, somewhat disagree 6% strongly disagree 4%. An economist claims that the distribution of the opinions of the opinions of US teenagers is different from the distribution opinions of US parents. To test the economist randomly selected 200 US teenagers and asked each whether a college education is worth the expense. The table shows the results. At level of significance of 5%, is there enough evidence to support the economist’s claim?

Response	Frequency
Strongly Agree	86
Somewhat Agree	62
Neither Agree nor Disagree	34
Somewhat Disagree	14
Strongly Disagree	4

Answer 1

The expected frequency for each category here is computed as:
E_i = p_i * 200 where p_i is the expected frequency from the known opinions of US parents on whether a college education is worth the expense

After this the chi square test statistic contribution for each category is computed here as:

Response	O_i	E_i	(E_i - O_i)^2/E_i
Strongly Agree	86	110	5.236
Somewhat Agree	62	60	0.067
Neither Agree nor disagree	34	10	57.600
Somewhat disagree	14	12	0.333
Strongly disagree	4	8	2.000
	200	200	65.236

Summing up the last column, we get the required test statistic here as:

Df = n - 1 = 5 - 1 = 4

For 4 degrees of freedom, the p-value here is computed from the chi square distribution tables here as:

As the p-value here is approx. 0 < 0.05 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here and conclude that we have sufficient evidence here that  distribution of the opinions of the opinions of US teenagers is different from the distribution opinions of US parents