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Research Methods Homework 7: 2 Test for Categories When submitting this homework assignment to the dropbox “Homework 7” folder, name the file using the following format: HW7_your_name.docx (e.g. HW7_Sed_Keller.docx). Assignment Purpose: This assignment will familiarize you with a common statistical test used in the scientific studies. As scientists, we require a basic understanding of statistics in order to draw conclusions from our data. Problem The goal of this problem is to derive and then apply a 2 test. Imagine you ask a sample of N people their opinion about a topic. There are d possible answers they might give you. For instance, you ask 200 students so N = 200. You expect that a proportion μi of these people will give you answer i. For instance, you expect 25 % of the students are seniors, so i = “senior” and μi = 0.25 (a) What is the number of people Ei you expect to give answer i? Write down the formula, using the symbols above. Ei = ... (b) In your actual data, you observe that a proportion X i actually gives you answer i. For example, 20 % answer “Yes” to your first question. In general what is the observed number of people i you observe giving answer i? Write down the formula using symbols from above. i = . .. (3.58) To compute 2 you need to know the standard error associated with measuring X i. Statisticians have found that when N people choose result i with probability μi, the standard error involved in measuringX i is i i / ; (3.59) that is, the uncertainty in the fraction X i is it. N being large, but you can use i / This result is approximate, and depends upon To get a more usable formula for use with surveys, do the following steps: (c) Write down the formula for 2 in Equation 3.50 2. . . (3.60) Research Methods Homework 7: Chi Square Test for Categories (d) Rewrite the formula, substituting in the expression for standard error from Equation 3.59. (e) The square-root and squared term in the denominator cancel out so... (f) Bring the term N up to the numerator. (g) Bring the N in the numerator inside the squared term. To do that, multiply the whole equation inside the summation symbol by 1 (h) Now bring the N inside the parentheses in the numerator. You should now have a formula that looks like: 2 i i i2 i (3.61) (i) Obtain Equation 3.52. Page 2 of 2