Changes in Education Attainment: According tothe U.S. Census Bureau, the distribution of Highest EducationAttainment in U.S. adults aged 25 - 34 in the year 2005 isgiven in the table below.
Census: Highest Education Attainment - 2005
| 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, thecounts for these levels of educational attainment are given in thetable below.
Survey (n = 4000): Highest Education Attainment -2013
| No | High School | Associate's | Bachelor's | Graduate or |
| Diploma | Diploma | Degree | Degree | Professional Degree |
| Count | 485 | 1922 | 336 | 876 | 381 |
|
The Test: Test whether or not the distribution ofeducation attainment has changed from 2005 to 2013. Conduct thistest at the 0.01 significance level.(a) What is the null hypothesisfor this test?
H0: p1 = p2 =p3 = p4 = p5 = 1/5H0: The probabilities are not all equal to1/5. H0: p1= 0.14, p2 = 0.48, p3 = 0.08, p4 =0.22, and p5 = 0.08. H0: Thedistribution in 2013 is different from that in 2005.
(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 asother entries for that column.
| Highest | Observed | Assumed | Expected | |
| i | Education | Frequency(Oi) | Probability(pi) | FrequencyEi | |
| 1 | No Diploma | 485 | 0.14 | 560 | 2 |
| 2 | Diploma | 1922 | 0.48 | 3 | 0.002 |
| 3 | Associate's | 336 | 4 | 320 | 0.800 |
| 4 | Bachelor's | 5 | 0.22 | 880 | 0.018 |
| 5 | Grad orProf | 381 | 0.08 | 320 | 11.628 |
| | | |
| ? | | n = 4000 | | | ?2 = 6 |
|
(c) What is the value for the degrees of freedom? 7
(d) What is the critical value of
?2
? Use the answer found in the
?2
-table or round to 3 decimal places.
t? = 8
(e) What is the conclusion regarding the null hypothesis?
reject H0 fail to rejectH0
(f) Choose the appropriate concluding statement.
We have proven that the distribution of 2013 educationattainment levels is the same as the distribution in 2005. The datasuggests that the distribution of 2013 education attainment levelsis different from the distribution in 2005. There is not enough data to suggest thatthe distribution of 2013 education attainment levels is differentfrom the distribution in 2005.
