Question

the population, the standartized tests have a mean score of 870 points and a standard deviation of 71 points. Let SmailClass denote a binary variable equal to 15 if student is assigned to a small class and equal to 0 otherwise. A regression of Tessicore on SmaniClass yields TetScore =862.9+133× SmanClass, R2=0.03, SER =701 (1.5) ​ (2.4) ​​ Do small dasses improve lest scores? By how much? is the effect large? The estimated gain trem being in a small class is points, (Round your response to one decimal place) The mili and alternative trpotheses are: H0​λ1​=0 versus H1​λ1​=0

Answer 1

Assignment to a small class is associated with an increase in test scores by 133 points, as indicated by the coefficient in the regression equation. The small R-squared value suggests that class size is not the sole factor impacting test scores. The hypothesis test for this regression coefficient entails comparing the null hypothesis of no effect to the alternative hypothesis of a non-zero effect.

Step-by-step explanation:

Based on the regression equation TetScore = 862.9 + 133 × SmanClass, we can see that being in a small class (where SmanClass = 1) is associated with an increase in the test score by 133 points. The reported coefficient for SmanClass is statistically significant given the t-values provided (2.4). However, considering the R-squared value of 0.03, the effect explains only 3% of the variation in test scores, suggesting that other factors also play a significant role in determining test scores.

The null and alternative hypotheses for this regression coefficient would be H0: λ1 = 0 (no effect of being in a small class on test scores) versus H1: λ1 ≠ 0 (there is an effect of being in a small class on test scores).