A researcher employed by the state department of education in a state with a large proportion of students coming from families in which English is not the primary language spoken at home is asked to assess a new program to teach written English to fifth- grade students. She obtains the scores on a statewide language test for 500 fifth- grade students after a year in the new program and for 500 students that were not in the program. Let S be the scores on the exam for the 1,000 students. The following model was used to assess the effectiveness of the new program.

S = β₀ + β₁P + β₂E + β₃P^* E + ɛ

a. Display the mean score for each of the four groups of students ( new program English spoken at home, old program' English spoken at home, etc.) in terms of the bs in the above model.
b. The researcher wanted to compare the mean scores of students in the new and old programs. She decided it would be necessary to separate the students from homes in which English was spoken from the students from homes in which English was not spoken. For those students whose families did not speak English at home, express the difference in mean scores in terms of the βs in the above model between students who were in the new program and those who were in the old program.
c. For those students whose families spoke English at home, express the difference in mean scores in terms of the bs in the above model between students who were in the new program and those who were in the old program.
d. Explain why it is necessary to include the term b3P* E in the model.

Transcribed Image Text:

English spoken at home English not spoken at home 1 if 1 f new program P-to i old program 0 if