Question

Comparing private and public college tuition. According to the Chronicle of Higher Education Almanac, 4-year private colleges charge, on average, five times as much for tuition and fees than 4-year public colleges. In order to estimate the true difference in the mean amounts charged for an academic year, random samples of 40 private colleges and 40 public colleges were contacted and questioned about their tuition structures.

1. Which of the procedures described in Chapter 8 could be used to estimate the difference in mean charges between private and public colleges?
2. Propose a regression model involving the qualitative independent variable type of college that could be used to investigate the difference between the means. Be sure to specify the coding scheme for the dummy variable in the model.
3. Explain how the regression model you developed in part b could be used to estimate the difference between the population means.

Short answer

1. The method of independent sampling to find the difference between two population means would be used here.
2. The regression model can be written as$E\left(y\right)={\beta }_0+{\beta }_1{x}_1$where x₁ denotes the type of college.
3. The estimated regression model developed in part b can be used to infer conclusions about the population means. When x₁ = 1,$E\left(y\right)={\beta }_0+{\beta }_1$and when x₁ = 0 (meaning private college charges) which is taken as the base level here, E(y) = β_0.Therefore, for x₁ = 1, $E\left(y\right)={\beta }_0+{\beta }_1$denotes the mean difference in the charges between private and public colleges.

Step-by-step solution

Difference between private and public college charges

The method of independent sampling to find the difference between two population means would be used here.

Regression model

Here to find a model indicating difference between means of private and public college charges a qualitative variable; x₁; to denote the type of college is introduced where

X₁ = 1, if private college

0, if public college

The regression model can be written as . $E\left(y\right)={\beta }_0+{\beta }_1{x}_1$

Difference between population means

The estimated regression model developed in part b can be used to infer conclusions about the population means.

When x₁ = 1,$E\left(y\right)={\beta }_0+{\beta }_1$and when x₁ = 0 (meaning private college charges) which is taken as the base level here, E(y) = β₀

Therefore, for x₁ = 1, $E\left(y\right)={\beta }_0+{\beta }_1$denotes the mean difference in the charges between private and public colleges.