LAB 5 Finished

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LAB 5: Testing Hypotheses using statistics (difference of 2 proportions & chi-square) 10/23/23 DUE BY 10/23/23 at 11:59 PM 5 points off each day it’s late Submit this document (or another document with your answers) and excel, Graded out of 100 points, Excel file is worth 40 points It has been shown that students with parents who graduated from college, are more likely to graduate from college themselves. The ELS (Education Longitudinal Study) is a nationally representative survey of students across the United States; it surveys students, parents, and teachers. Suppose we want to understand the mechanisms by which parents’ education status impacts their students’ educational attainment. One approach is to think about whether parents with higher levels of educational attainment have higher expectations or aspirations for their children, in terms of educational attainment. For example, is a parent with a bachelor’s degree more likely to expect their child to earn a bachelor’s degree than a parent who did not go to college? This is especially important to understand as we try to uncover what impacts students’ college-going and degree attainment. In the dataset, parents are asked: How far do you expect your 10 th grader to go? And are given the following options to choose from: Don’t know, Less than HS graduation, High school graduation or GED only, Attend or complete 2-year college, Attend college (4-year incomplete), Graduate from college (4-year), Obtain Master’s or equivalent, Obtain PhD or MD or other advanced degree Codebook: Parent_expect_collgrad= 0 when a parent does not expect at least a 4-year college degree, and 1 if they expect at least a 4-year degree (or more). Parent_collgrad= 0 when parent has less than a 4-year college degree, and 1 if a parent has a BA degree or more, Question #1: Examine the construct validity of this measure (parent expectations). Use full sentences. Construct validity: refers to the degree to which a test of measurement accurately assesses the underlying theoretical construct it intends to measure. In this case- does the chosen measure actually measure parent expectations (something that is hard to measure). 5 points

- I think that this measure has a strong construct validity to a strong degree. Problems that can arise from this is that this sample is taken while students are in 10 th grade. This leaves still 2-3 years for students to grow and parents to be able to understand the path that is best fitting for their child. The hypotheses are: Null: There is no difference in parent expectations of students for parents with and without a bachelor’s degree. H 0 : p 1 − P 2 = 0 Alternative: There is a relationship between parent expectations of students and parent educational attainment H 0 : p 1 − P 2 = 0 Question #2: What do p 1 and P 2 represent in the hypotheses above? 4 points (2 each) - P1 represents the first population sample taken within the hypothesis and the P2 is the second population sample taken within the hypothesis. Part A: Difference of 2 proportions Use Part A sheet Step 1: Calculate proportions Let’s start by creating a table that shows the raw numbers for each proportion. Enter this table into excel in an empty set of cells (do not include Value1-4 in table, this is just to label where to put certain equations). Expects student to graduate college? Yes No Parent has BA Value 1 Value 3 Parent does not have BA Value 2 Value 4 Now let’s fill in the table in excel as follows: We want to calculate counts using the =COUNTIFS function. The COUNTIFS function tell us to count the number of cells that have a particular value in a certain cell range  =COUNTIFS(starting cell : ending cell, value). If we want to count based on two conditions we just add a comma after the first specified value, and then include another starting cell : ending cell, value, like so: =COUNTIFS(start cell 1: end cell 1, value 1, start cell 2: end cell 2, value 2)

For Value 1, we want to write =COUNTIFS(A2:A12263, 1, B2:B12263, 1) Value 2, =COUNTIFS(A2:A12263, 1, B2:B12263, 0) Value 3 =COUNTIFS(A2:A12263, 0, B2:B12263, 1) Value 4 =COUNTIFS(A2:A12263, 0, B2:B12263, 0) Question 3: Explain what one of the COUNTIFS equations is doing. For example, in Value 1 we are… 5 points - For value 1 we are counting if the parent does have a BA degree and they expect the students to graduate. Now we can generate the pooled proportion we need to test the success-failure condition We want to calculate: Totalsuccesses Total cases  Total ¿ of parentsthat expect kids ¿ earnBA ( at least ) ¿ Total ¿ of parents ¿  Value 1 + Value 2 Value 1 + Value 2 + Value 3 + Value 4 Question 4: What is the pooled proportion (the ratio/number found)? 3 points - 0.77092 Step 2: Success-failure condition We want to make sure we meet the success/failure condition to ensure we have a sufficient sample size. We can do this in excel! The formula is: n p 0 ≥ 10 ∨ n ( 1 − p 0 ) ≥ 10 n = sample size p 0 = null hypothesis proportion We have to do this for both proportions In excel, in an empty cell, we can multiply the sample size by the null proportion, as follows: 1. (1-.77) * 5426 2. (1-.77) * 7016 Question 5: How did I get 5246 and 7016? 5 points What estimates did you find? 4 points (2 each) Does this satisfy the success/failure condition? 2 points

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