Changes in Education Attainment: According to the U.S. Census Bureau, the distri
ID: 3231733 • Letter: C
Question
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
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
The Test: Test whether or not the distribution of education attainment has changed from 2005 to 2013. Conduct this test at the 0.01 significance level.
(a) What is the null hypothesis for this test?
H0: p1 = 0.14, p2 = 0.48, p3 = 0.08, p4 = 0.22, and p5 = 0.08.
H0: The distribution in 2013 is different from that in 2005.
H0: p1 = p2 = p3 = p4 = p5 = 1/5
H0: The probabilities are not all equal to 1/5.
(b) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.
(c) What is the value for the degrees of freedom? _______________
(d) What is the critical value of 2 ? Use the answer found in the X2 -table or round to 3 decimal places.
t = _____________
(e) What is the conclusion regarding the null hypothesis?
reject H0
fail to reject H0
(f) 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.
No High School Associate's Bachelor's Graduate or Diploma Diploma Degree Degree Professional Degree Percent 14% 48% 8% 22% 8%Explanation / Answer
(a)Null hypothesis for this test?
H0: p1 = 0.14, p2 = 0.48, p3 = 0.08, p4 = 0.22, and p5 = 0.08
(b)
i
Education
Frequency (Oi)
Probability (pi)
Frequency Ei
(Oi Ei)2
Ei
1
No Diploma
535
0.14
560
0.116
2
Diploma
1922
0.48
1920
0.002
3
Associate's
336
.08
320
0.800
4
Bachelor's
881
0.22
880
0.001
5
Grad or Prof
326
0.08
320
0.113
n = 4000
2 = 1.032
c) Value for the degrees of freedom= 5-1=4
(d) The critical value of 2 = 13.277 (at 0.01 level of significance)
(e) The conclusion regarding the null hypothesis?
Fail to reject H0
Since calculated 2 (1.032) < critical value of 2 at 0.01 (13.277)
(f) Concluding statement is
There is not enough data to suggest that the distribution of 2013 education attainment levels is different from the distribution in 2005.
(b)
i
Education
Frequency (Oi)
Probability (pi)
Frequency Ei
(Oi Ei)2
Ei
1
No Diploma
535
0.14
560
0.116
2
Diploma
1922
0.48
1920
0.002
3
Associate's
336
.08
320
0.800
4
Bachelor's
881
0.22
880
0.001
5
Grad or Prof
326
0.08
320
0.113
n = 4000
2 = 1.032
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