**The Cost of Attending College and Its Influences**The cost of attending college has increased, despite being viewed as an investment in human capital. A study was conducted to examine how various factors influence college costs, particularly focusing on university reputation. Data was collected for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report rankings. A regression analysis was performed:\[ \text{Cost} = 7,311.17 + 3,985.20 \times \text{Reputation} - 0.20 \times \text{Size} + 8,406.79 \times \text{Dpriv} - 416.38 \times \text{Dlibart} - 2,376.51 \times \text{Dreligion} \]\[R^2 = 0.72, \text{ SER } = 3,773.35\]**Variables Defined:**- **Cost**: Tuition, fees, room, and board in dollars.- **Reputation**: Ranked from 1 ("marginal") to 5 ("distinguished").- **Size**: Number of undergraduate students.- **Dpriv**, **Dlibart**, **Dreligion**: Binary indicators for private, liberal arts, and religious affiliations.**Standard Errors** (in parentheses): - Heteroskedasticity-robust standard errors are provided.**Questions Analyzed:**(a) **Significance of Size**: - Calculate the t-statistic for the coefficient on Size using the standard normal table to determine if it is statistically significant at the 5% level.(b) **F-Test for Hypotheses**:- Simultaneously test if coefficients for Size and Dlibart are zero.- Use F-statistics (F = 1.23) against the critical value at the 5% level to determine if you can reject the null hypothesis.**Graph Explanation:**- **F Distribution Graph**: A curve illustrates the area corresponding to significance levels.- Critical values of F for different significance levels and degrees of freedom are tabulated.This analysis aims to discuss the multifaceted influences on college costs and provide insights into statistical testing in the context of higher education research.

The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you perform the following regression Cost = 7,311.17 +3,985.20 × Reputation - 0.20 × Size +8,406.79 x Dpriv-416.38 x Dlibart-2,376.51 x Dreligion (2,058.63) (664.58) (0.13) (2,154.85) (1,007.86) R2 = 0.72, SER= 3,773.35 (1,121.92) where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers), which ranges from 1 ("marginal") to 5 ("distinguished"), Size is the number of undergraduate students, and Dpriv, Dlibart, and Dreligion are binary variables indicating whether the institution is private, a liberal arts college, and has a religious affiliation. The numbers in parentheses are heteroskedasticity-robust standard errors. (a) Referring to the standard normal table: standardnormaltable.pdf, the coefficient on Size carries a t-statistic of - Hint: Type a number in two decimal places. Hence is not statistically significant at the largest integer among 10, 5, and 1. (b) You want to test simultaneously the hypotheses that BSize = 0 and BDilbart = 0. The number of restrictions for your F-test is Hint: type an integer. decimal places. % level (using a one-sided alternative hypothesis). Hint: type a Your regression package returns the F-statistic of 1.23. The critical value of F-statistic is at 1% level. Hence you cannot reject the null hypothesis in this case. at 5% level and Hint: type numbers in two