Final answer:
The assumption that the error terms in simple regression analysis are exponentially distributed is false; instead, they are assumed to be normally distributed. For hypothesis testing in regression, the normal distribution is commonly used as the exact distribution for the test statistic, especially for large samples. False.
Step-by-step explanation:
One of the assumptions of simple regression analysis is that the error terms are exponentially distributed. This statement is false. In simple linear regression, the assumption is that the error terms are normally distributed with a mean of zero and a constant variance (homoscedasticity).
If the error terms were exponentially distributed, this would imply a specific, non-normal distribution of errors which is not assumed in traditional simple regression analysis. Instead, for conducting hypothesis tests with regression analysis, the assumed distribution of the test statistic under the null hypothesis is typically the t-distribution for small samples or the normal distribution for larger samples. This assumption is key to deriving the confidence intervals and conducting tests of significance for regression coefficients.
To answer the related multiple-choice question referring to the exact distribution for the hypothesis test, the correct answer would be a. the normal distribution, considering the sample is large enough, typically greater than 30. This aligns with the central limit theorem, which states that the sampling distribution of the sample means approaches a normal distribution as the sample size grows.