When the confidence level of a test is increased which of the following will happen –
First, the core concept would be statistical hypothesis testing and confidence intervals. When confidence level increases, like from 95% to 99%, the confidence interval becomes wider. This is because higher confidence requires a larger range to capture the true parameter, which increases the chance of including the true value.
Why is that? Well, the confidence interval is calculated using a critical value (like z or t) that depends on the confidence level. A higher confidence level means a higher critical value (e.g., z=1.96 for 95% vs. z=2.58 for 99%), leading to a wider interval. So the correct answer would be that the confidence interval becomes wider.
Now, the incorrect options. Let's say the options were about the p-value, type I error, or sample size. For example, if an option says "p-value decreases," that's incorrect because the p-value is determined by the data, not the confidence level. Another option might be "type I error decreases," which is true because a higher confidence level (like 99%) corresponds to a lower alpha (1% vs. 5%), thus reducing the chance of type I error. Wait, but if the confidence level increases, the alpha (significance level) decreases. So if the question is about what happens when confidence level increases, then the correct answer is the confidence interval widens. Other options might be about the margin of error increasing, which it does because the critical value is larger. So the margin of error increases, making the interval wider.
Clinical pearl: Remember that higher confidence = wider interval. Don't confuse confidence level with p-value; they are different concepts. Also, increasing confidence level reduces the risk of type I error (since alpha is smaller), but increases the risk of type II error if sample size isn't adjusted.
Putting it all together, the explanation should cover these points concisely. Need to check the structure: Core Concept, Why Correct, Why Wrong, Clinical Pearl, Correct Answer line. Make sure each section is within the character limit and uses proper markdown.
**Core Concept**
Confidence level in statistical testing refers to the probability that a confidence interval will contain the true population parameter. Increasing the confidence level (e.g., from 95% to 99%) affects the width of the confidence interval and the risk of type I error.
**Why the Correct Answer is Right**
A higher confidence level requires a wider confidence interval to ensure the true population parameter is captured with greater certainty. This occurs because the critical value (e.g., z-score or t-score) increases, expanding the margin of error. For example, a 99% confidence interval uses a z-score of 2.58 compared to 1.96 for 95%, directly widening the interval.
**Why Each Wrong Option is Incorrect**
**Option A:** *Type I error increases* β Incorrect. A higher confidence level reduces the significance level (Ξ±), decreasing the risk of type I error.
**Option B:** *Type II error decreases* β Incorrect. While type II