Question

A previous researcher has published a report demonstrating that students’ interest in studying mathematics is related to his or her interest in general academics. Furthermore, this researcher also claimed that interest in studying English-related subjects (literature, journalism, etc.) was not related to interest in mathematics. However, after reading the article, you believe the findings contradict your experience, and you believe there was a methodological flaw in the analysis. In particular, you believe it was necessary for the researcher to have accounted for another variable: school year.

Your plan is to collect a small data set from 2 groups of students. Your research questions are based around the hypothesis that the relationship between interest in mathematics and interest in both academics & English subjects is moderated by school year.

Using the same measurement scales for interest as the first researcher, you collect data from two groups. The first group is all year-8 students. The second group is all year-10 students. You will now run a multiple regression analysis using the interest in general academics and English classes as the independent variables and interest in mathematics as the dependent variable. For this analysis, you should use a significance level of α=0.05α=0.05.

GROUP-1 Year-8 Students	GROUP-2 Year-10 Students
Interest in General Academics Interest in English Classes Interest in Studying Mathematics 36.9 56 35.2 37.6 63.3 53.4 41.4 75 48.3 41.6 70.4 52 41.7 44.2 31.6 42.2 54.3 44.7 33.9 48.1 42.1 53 42 48 39.9 54.5 55.2 42.6 69.9 63.4 40.6 55.4 39.2 40.7 39.2 46.2 53 42.9 46.6 34.4 47.4 44.7 40.4 58.1 42.9 26.7 32.2 33.1 39.7 64 46.6 43 50.7 46.3 49.2 61.1 51.9 34.7 52.4 53.3	Interest in General Academics Interest in English Classes Interest in Studying Mathematics 51.8 40.3 54.6 51.2 68.2 49.2 49.2 48 63.4 58.3 29.6 73.3 45.7 55.5 52.1 53.8 54.4 56.5 39.5 45.6 54.7 40.6 42.2 61.8 52.3 59.2 45.2 49.8 36 63.3 52.4 48.1 61.9 36.8 48.1 56.2 45.4 62.1 52.9 45.2 49.1 65.1 60.8 52.3 58 36.2 53.9 56.5 41 52.8 56.1 55.8 57.1 41.6 50.8 51.2 43.1 52.9 52.6 58.3

( 1a ) When examining the first group (year-8), what is the estimated value for the influence of interest in general academics on interest in mathematics (after accounting for interest in English classes)?

(Report answer accurate to 3 decimal places.)

( 1b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 1c ) For the year-8 group, is the influence of interest in general academics on interest in mathematics statistically significantly different from zero?

• yes
• no

( 2a ) When examining the first group (year-8), what is the estimated value for the influence of interest in English classes on interest in mathematics (after accounting for interest in general academics)?

(Report answer accurate to 3 decimal places.)

( 2b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 2c ) For the year-8 group, is the influence of interest in English classes on interest in mathematics statistically significantly different from zero?

• yes
• no

( 3a ) When examining the second group (year-10), what is the estimated value for the influence of interest in general academics on interest in mathematics (after accounting for interest in English classes)?

(Report answer accurate to 3 decimal places.)

( 3b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 3c ) For the year-10 group, is the influence of interest in general academics on interest in mathematics statistically significantly different from zero?

• yes
• no

( 4a ) When examining the second group (year-10), what is the estimated value for the influence of interest in English classes on interest in mathematics (after accounting for interest in general academics)?

(Report answer accurate to 3 decimal places.)

( 4b ) What is the p-value for this slope?   
(Report answer accurate to 4 decimal places.)

( 4c ) For the year-10 group, is the influence of interest in English classes on interest in mathematics statistically significantly different from zero?

• yes
• no

Answer 1

For this problem we will be using the R software.

FOR GROUP 1

(1a) The estimated value for the influence of interest in general academics on interest in Mathematics is 0.314.

(1b) The p-value for this slope is 0.214.

(1c) Our level of significance is 0.05. Since p-value = 0.214 > 0.05, our null hypothesis which states that effect of interest in General Academics on interest in Mathematics is 0, stands accepted. Hence for the year-8 group, the influence of interest in general academics on interest in Mathematics is not significantly different from zero.

(2a) The estimated value for the influence of interest in English on interest in Mathematics is 0.361.

(2b) The p-value for this slope is 0.0160.

(2c) Our level of significance is 0.05. Since p-value = 0.016 < 0.05, our null hypothesis which states that effect of interest in English on interest in Mathematics is 0, stands rejected. Hence for the year-8 group, the influence of interest in general academics on interest in Mathematics is statistically significantly different from zero.

FOR GROUP 2

(3a) The estimated value for the influence of interest in general academics on interest in Mathematics is -0.042.

(3b) The p-value for this slope is 0.8308.

(3c) Our level of significance is 0.05. Since p-value = 0.8308 > 0.05, our null hypothesis which states that effect of interest in General Academics on interest in Mathematics is 0, stands accepted. Hence for the year-10 group, the influence of interest in general academics on interest in Mathematics is not significantly different from zero.

(4a) The estimated value for the influence of interest in English on interest in Mathematics is -0.604.

(4b) The p-value for this slope is 0.0010.

(4c) Our level of significance is 0.05. Since p-value = 0.001 < 0.05, our null hypothesis which states that effect of interest in English on interest in Mathematics is 0, stands rejected. Hence for the year-10 group, the influence of interest in general academics on interest in Mathematics is statistically significantly different from zero.