Education. Post-secondary educationalinstitutions in the United States (trade schools, colleges,universities, etc.) traditionally offer four different types ofdegrees or certificates. The U.S. Department of Education recordedthe highest degree granted by each of these institutions in theyear 2003. The percentages are shown in the table below. A randomsample of 225 institutions was taken in 2013 and the number ofinstitutions in the sample for each category is also shown in thetable. Conduct a hypothesis test to determine whether there hasbeen any change from the percentages reported in 2003. Round allcalculated values to four decimal places.
| Highest Degree Awarded | Population percentages in 2003 | Sample counts in 2013 |
| Certificate | 35.0% | 80 |
| Associates | 26.6% | 54 |
| Bachelor's | 11.3% | 28 |
| Graduate | 27.1% | 63 |
a. Enter the expected values for the hypothesis test in thetable below.
| Highest Degree Awarded | Expected value |
| Certificate | |
| Associates | |
| Bachelor's | |
| Graduate | |
b. Calculate the test statistic for this hypothesistest.  ? z t X^2 F  =
c. Calculate the degrees of freedom for this hypothesistest.
d. Calculate the p-value for this hypothesis test. p-value =
e. Based on the p-value, we have:
A. little evidence
B. strong evidence
C. very strong evidence
D. some evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.
