Define Type I and Type II errors in hypothesis testing and explain their implications.

Type I and Type II Errors in Hypothesis Testing: In hypothesis testing, Type I and Type II errors represent two different ways in which we can make incorrect decisions regarding the acceptance or rejection of a null hypothesis. These errors have distinct implications for the validity of a hypothesis test and the potential consequences of those errors. 1. Type I Error (False Positive): - Definition: A Type I error occurs when we incorrectly reject a null hypothesis that is actually true. In other words, it's a "false positive" or a "false alarm." - Symbol: Often denoted as α (alpha), the significance level, which represents the probability of making a Type I error. - Implications: - Type I errors are considered more serious in situations where the null hypothesis represents a default or conservative position. For example, in medical testing, a Type I error may lead to the incorrect rejection of a safe and effective treatment. - Lowering the significance level (α) reduces the probability of Type I errors but increases the risk of....