Question

4 Changes in Education Attainment: According to the U.S. Census Bureau, the distribution of Highest Education Attainment in U.S. adults aged 25 - 34 in the year 2005 is given in the table below. Census: Highest Education Attainment - 2005 i 1 2 3 4 5 No High School Associate's Bachelor's Graduate or Diploma Diploma Degree Degree Professional Degree Percent 14% 48% 8% 22% 8% In a survey of 4000 adults aged 25 - 34 in the year 2013, the counts for these levels of educational attainment are given in the table below. Survey (n = 4000): Highest Education Attainment - 2013 i 1 2 3 4 5 No High School Associate's Bachelor's Graduate or Diploma Diploma Degree Degree Professional Degree Count 523 1922 346 886 323 The Test: Test whether or not the distribution of education attainment has changed from 2005 to 2013. Conduct this test at the 0.05 significance level. (a) What is the null hypothesis for this test in terms of the probabilities of the outcomes? H0: p1 = 0.14, p2 = 0.48, p3 = 0.08, p4 = 0.22, and p5 = 0.08. H0: p1 = p2 = p3 = p4 = p5 = 1/5 H0: The probabilities are not all equal to 1/5. H0: The distribution in 2013 is different from that in 2005. (b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places. χ2 = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0 (e) Choose the appropriate concluding statement. We have proven that the distribution of 2013 education attainment levels is the same as the distribution in 2005. The data suggests that the distribution of 2013 education attainment levels is different from the distribution in 2005. There is not enough data to suggest that the distribution of 2013 education attainment levels is different from the distribution in 2005.

Answer 1

a) The null hypothesis is :

	No Diploma	High School Diploma	Associate's Degree	Bachelor's Degree	Graduate or Professional Degree	Total
Count	523	1922	346	881	328	4000
Expected Count	0.14*4000=560	0.48*4000=1920	0.08*4000=320	0.22*4000=880	0.08*4000=320	4000
Count - Expected Count	-37	2	26	1	8
	2.4445	0.002083333	2.1125	0.001136364	0.2	4.7603

c) P-value =0.31278

d)

e) There is not enough data to suggest that the distribution of 2013 education attainment levels is different from the distribution in 2005.