The probability that a randomly chosen student at the University ofNew Harmony is a women is 0.6. The probability that the student isstudying education is 0.15. The conditional probability that thestudent is a women, given that the student is studying education is0.8. What is the conditional probability that the student isstudying education, given that she is a women?
QUESTION 5 Regarding the Chi-Square test for frequencies, which of the following is false? 1. The most frequent use of the chi-square distribution is in the analysis of nominal data. 2. Observed frequencies are obtained empirically through direct observations. 3. Expected frequencies are developed on the basis of some theory or hypothesis. 4. The chi-square test, which is a nonparametric test, has more restrictive assumptions than parametric tests.1. (16 points) Olive has the utility function U(X, Y) = X1/3y2/3, where X is the quantity of apples consumed, and Y is the quantity of oranges consumed. Let income be I = 90. (a) Suppose that the price of apples is Po = 2 and the price of oranges is Py = 2. What are the quantities of apples and oranges demanded when Olive maximizes her utility subject to her budget constraint? (b) Suppose that the price of apples decreases to Py = 1 and the price of oranges stays constant at Py = 2. What are the quantities of apples and oranges demanded by Olive after this price change? (c) What is the substitution effect from the price change above? Hint: what is the ex- penditure minimizing way of achieving the utility level in part (a) at the prices in part (b)? ] (d) What is the income effect from the price change above? [Hint: what is the difference between the total effect in part (b) and the substitution effect in part (c)?]9. Consider the chi-square analyses we discussed in Unit 5. a. Describe how you determine expected values for a univariate chi-square test? (2 marks) b. How do you interpret a statistically significant univariate chi-square? Include formulae if needed. (5 marks) C. Describe how you determine the expected values for a bivariate chi-square test? (2 marks) d. How do you interpret a statistically significant bivariate chi-square? Include formulae if needed. (5 marks) e. Is the McNemar test a univariate or a bivariate chi-square analysis? (2 marks) Why? (2 marks) f. How do you determine the expected values for a McNemar test? (2 marks) Why are the expected values derived in this way? (3 marks) g. How is a statistically significant McNemar test interpreted? Include formulae if needed. (5 marks)Chi-Square: Assume that the last 20 children born at a Hospital were 15 Boys and five Girls. Use the Chi-Square test to determine whether these data represent a 50/50 sex-ratio. State your null and alternative hypotheses, expected and observed values, degrees of freedom, calculated chi-square value, interpretation of your chi- square test, and your theoretical conclusion, for N=20, Alpha= 0.05 and Critical Chi-Square = 3.84
