ECON 266: Hypothesis Testing

In the context of Ordinary Least Squares (OLS) estimation, what is the MOST critical condition to satisfy in order to ensure that the resulting estimator is considered 'best' in the Best Linear Unbiased Estimator (BLUE) sense, assuming all other classical assumptions hold?

When initiating a quest for causality using observational data and employing Ordinary Least Squares (OLS) within a regression framework, what fundamental assumption MUST be stringently addressed to ensure that the estimated parameters can be interpreted as causal effects rather than mere associations?

When assessing the impact of a Quasi-Experimental Research (QSR) facilitated study group on student grades using a bivariate Ordinary Least Squares (OLS) model, what specific econometric challenge is MOST likely to confound the interpretation of the estimated coefficient on the QSR variable as a causal effect?

In the context of hypothesis testing within an econometrics framework, if the null hypothesis posits 'no effect' (β₁ = 0), what Bayesian interpretation can be drawn regarding the probability of observing a sample estimate (b₁) that deviates substantially from zero?

When interpreting Ordinary Least Squares (OLS) regression results, under what specific condition would rejecting the null hypothesis MOST strongly suggest a statistically significant relationship between the independent and dependent variables, assuming a pre-specified significance level?

Within the classical Null Hypothesis Significance Testing (NHST) tradition, what inferential leap is made when a researcher confidently rejects the null hypothesis at a predetermined significance level (alpha), and what philosophical caveat MUST accompany this conclusion?

Under what condition would a researcher opt for a one-sided alternative hypothesis over a two-sided alternative hypothesis when conducting a hypothesis test, explicitly acknowledging the inherent risks and limitations involved in the selection process?

In the context of hypothesis testing, what fundamental trade-off exists when a researcher decides to decrease the significance level (alpha) from 0.05 to 0.01, and how does this decision impact the probabilities of Type I and Type II errors, considering practical implications?

In the context of statistical hypothesis testing, differentiate between a Type I error and a Type II error, and explore the practical and ethical ramifications of committing each type of error in a real-world scenario such as evaluating the efficacy of a novel pharmaceutical intervention.

Considering the profound implications of both Type I and Type II errors, what multifaceted strategy can a researcher employ to minimize the risk of committing either type of error, explicitly acknowledging the limitations and trade-offs inherent in this process?

What is the most precise definition of a null hypothesis ($H_0$) in the context of econometrics, and how does it fundamentally shape the framework for statistical inference and decision-making?

In what critical sense does statistical methodology prevent us from definitively 'proving' or 'disproving' a null hypothesis, and what nuanced approach MUCH be adopted when interpreting the outcomes of hypothesis tests within this constraint?

What inferential errors are we exposed to when rejecting a null hypothesis ($H_0$), and explain what specific condition MUST be present when this can be labeled as a 'statistically significant' result?

In the presence of a statistically significant coefficient in an Ordinary Least Squares (OLS) regression, how is this significance determined and what does it imply about the variability of the estimated coefficient?

What is the quintessential difference between a Type I and a Type II error in the context of hypothesis testing, and what are the consequential impacts of committing each of these particular error types?

In the context of impact evaluation, what are the potential pitfalls of committing either a Type I or Type II error in evaluating the effectiveness of a new educational program such as the impact of QSR facilitated study groups?

How does the formulation of alternative hypotheses affect the process of hypothesis testing? Specifically, what is the key distinction between a one-sided and two-sided alternative hypotheses, and how is each appropriately used in empirical research?

When should a researcher opt for a one-sided alternative hypothesis ($H_A: β_1 > 0$ or $H_A: β_1 < 0$) over a two-sided alternative hypothesis ($H_A: β_1 ≠ 0$), and what considerations MUST guide this decision?

Why is a two-sided alternative hypothesis generally considered more 'cautious' than a one-sided alternative hypothesis?

How does the 'significance level' affect the decision to reject the null hypothesis, and what is implied from this interaction?

How does decreasing the value of $\alpha$ (significance level) affect the likelihood of committing Type I Errors and Type II Errors?

What is implied relative to the central limit theorem by the Student's t-distribution? Specifically, what are the relationships and differences?

How does the t stat affect the rejection of the null hypothesis?

A researcher finds a t stat of 1.73 given 20 degrees of freedom. In a two-tailed test using a 0.05 significance level, what statistical recommendation should be made? Refer to the critical values chart on slide 25.

In reviewing the test output data included in this output:

reg price weight Source | SS df MS -------------+ Model | 1.84e+08 1 1.84e+08 Residual | 4.51e+08 72 6261548.0 -------------+ Total | 6.35e+08 73 8699526.0 What statistical conclusion can be made measuring the coefficient and standard error relative to each other?