Question

• summarize chichewa_score math_score english_score Variable Obs Mean Std. Dev. Min Max 0 chichewa_3-e math_score ! english_sc-e 5,268 5,268 5,268 51.24468 44.88591 44.17122 22.54025 20.2357 20.10931 0 0 100 100 100 . correlate chichewa_score math_score english_score (obs-5,268) | chiche-e math_s-e englis-e chichewa_s-e math_score english_sc-e 1.0000 0.4909 0.6061 1.0000 0.5317 1.0000 Let's consider the hypothetical scenario in which the data in Q1 was collected differently. Assume that the Math and Chichewa scores were collected only from schools in Northern Malawi and English scores were collected only from schools in Southern Malawi. Hence, we have Math and Chichewa scores for a sample of students from Northern Malawi, and English scores for a sample of students from Southern Malawi. Answer the following questions in 1-3 sentences. (No new calculations required.) (a) [2 pts] What do you expect for the values of correlation between Math and English scores and Chichewa and English scores to be under this scenario? Why? (b) [2 pts] What would you expect to happen to the power of the hypothesis test you conducted in Q1? Why? 12 points) (c) (2 pts] Suppose you were now testing if the difference in the mean Chichewa and mean English scores in the new dataset was significant. Write down the appropriate formula for the degrees of freedom under this scenario. (You do not need to calculate the degrees of freedom.) (2 points)

Answer 1

(a) There is a moderate positive relationship between Math and English scores and also between Chichewa and English scores because a bright student would be able to score more in both Math and English.

(b) The power of the hypothesis would be medium effect size there is a moderate relationship between the variables.

(c) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

The df is 5268 + 5268 - 2 = 10534.