Which of the following descriptions of confidence intervals is correct? (Select all that apply)
a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
e. None of the above are correct about confidence intervals.
I Want to say E but i am having a hard time with all the confidence intervals. I understand that 95% means we are 95% positive and 99% means we are 99% positive but comparing them I want to say no. That if its a certain number at 95% then wouldn't the number increase at 99%.
The 99% confidence interval is wider than the 95%.
If something is in the 99% then it has to be in the 95% interval
Since it seems that a and d would be correct, it makes me think that your teacher is trying to show you that confidence intervals can always be different because you are taking different samples from the population. You can't say with certainty what will be in one confidence interval. The only way you could would be if you used the same data to make both the 95% and 99% confidence interval. If you took different samples then the answer would have to be e.
The correct answer is e. None of the above are correct about confidence intervals.
Confidence intervals are constructed based on a level of confidence, which represents the likelihood that the interval contains the true population parameter. Higher confidence levels, such as 99%, provide wider intervals, while lower confidence levels, such as 95%, provide narrower intervals.
The statements in options a, b, c, and d suggest an inverse relationship between confidence intervals of different levels, which is incorrect. For example, if a 95% confidence interval contains 0, it does not necessarily mean that the 99% confidence interval also contains 0. The confidence levels do not depend on each other in this manner.
So, in conclusion, none of the given options accurately describe the relationship between different confidence intervals.
To answer this question, we need to understand how confidence intervals work and how different confidence levels affect their widths.
A confidence interval is a range of values that we can be reasonably confident (to a certain level) contains the true population parameter based on a sample from the population.
Now let's evaluate each option:
a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0.
To check the validity of this statement, we need to understand that a higher confidence level results in a wider confidence interval because we are seeking a higher level of certainty. Therefore, if the 95% confidence interval contains 0, it is not necessarily the case that the 99% confidence interval will also contain 0. In fact, the 99% confidence interval is wider, so it may or may not include 0. Thus, option a is incorrect.
b. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0.
Similar to the previous option, if the 99% confidence interval contains 0, it doesn't necessarily mean that the 95% confidence interval will contain 0. The 95% confidence interval is narrower, so it is possible for it to exclude 0 while the wider 99% confidence interval includes 0. Therefore, option b is also incorrect.
c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1.
This statement is plausible given our understanding of confidence intervals. If the 95% confidence interval contains 1, it means that we are 95% confident that the true population parameter (such as the mean or proportion) lies within that range if we were to repeat the sampling process many times. Since the 99% confidence interval is wider, it is likely to include 1 as well. Therefore, option c could be correct.
d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1.
Similar to option c, if the 99% confidence interval contains 1, the wider interval suggests that the 95% confidence interval is likely to include 1 as well. Therefore, option d could also be correct.
Based on this analysis, we can see that options c and d are plausible, while options a and b are incorrect. Therefore, the correct answer is
c. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
d. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1.
It's important to note that this is a general explanation, and specific cases may vary depending on the calculations and assumptions made.