STEM Education: Another Look
- Due May 10, 2024 by 11:59pm
- Points 5
- Available until May 17, 2024 at 11:59pm
In a previous activity we looked at what Americans believed regarding the Quality of Education for STEM Careers Download Quality of Education for STEM Careers in 2018. The data came from Pew Social Trends Links to an external site..
The first table we studied reported "US Adults who rate the US when it comes to STEM Education at each level"
| Level of Education |
Consider Above Average |
Consider Average |
Consider Below Average |
Total |
|---|---|---|---|---|
|
K12 Public Schools |
25 |
44 |
31 |
100 |
|
Undergraduate |
35 |
47 |
18 |
100 |
|
Graduate |
38 |
44 |
18 |
100 |
|
Total |
98 |
91 |
67 |
300 |
We saw that each of the three levels of STEM education had a different probability of being rated above average, average, or below average. That seems to suggest that there is a relationship between the variables "level of STEM education" and "assessment of quality." In technical terms, it suggests that the two variables are NOT INDEPENDENT.
Question 1: Are the data from a SAMPLE or from a POPULATION? If from a sample, what population is implied?
Inferences from a Sample to a Population
These SAMPLE data come from the implied population "ALL US ADULTS." But if another sample of 300 adults were drawn randomly from the US adult population, we would not expect the numbers in the table to be the same. What we really want to know is whether the two variables are independent in the POPULATION. For that we need to make a statistical inference using the Chi-Squared Test of Independence.
The null hypothesis is that the two variables are INDEPENDENT in the population. The alternative hypothesis is that they are NOT INDEPENDENT in the population -- that is, a relationship exists. We will use a 5% level of significance.
Question 2: Conduct a Chi-Squared Test of Independence on the given data, using a 5% level of significance. Make sure to show all steps of a Hypothesis Test, including a clear statement of your conclusion.
The second table in the earlier activity contained data from a sample of US STEM Degree Holders (instead of from the US adult population as a whole).
| Level of Education |
Consider Above Average |
Consider Average |
Consider Below Average |
Total |
|---|---|---|---|---|
|
K12 Public Schools |
13 |
36 |
51 |
100 |
|
Undergraduate |
52 |
35 |
13 |
100 |
|
Graduate |
62 |
29 |
9 |
100 |
|
Total |
127 |
100 |
73 |
300 |
Question 3: Conduct a Chi-Squared Test of Independence (at a 5% level of significance) to decide whether or not the variables "level of STEM education" and "assessment of quality" are independent in the population of US STEM Degree Holders. Include all steps of a Hypothesis Test, including a clear statement of the result.
Now post in the Discussion: STEM Education
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