Identify each of the following statements as

omar aljaradi

omar aljaradi

Answered question

2022-05-09

Identify each of the following statements as true or false in relation to confidence intervals (CIs). 
Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.

 

 

 

 TrueFalse
A 95% CI is a numerical interval within which we are 95% confident that the true mean μμ lies.  
A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯x¯ lies.  
The true mean μμ is always inside the corresponding confidence interval.  
For a sample size n=29n=29, the number of degrees of freedom is n=30n=30.  
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would notnot contain the true mean 𝜇.  

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-06Added 106 answers

Let's identify each of the statements as true or false in relation to confidence intervals (CIs):
A 95% CI is a numerical interval within which we are 95% confident that the true mean μ lies.
This statement is true. A 95% confidence interval means that if we were to repeat the same experiment multiple times, the true population mean μ would lie within the interval in 95% of those repetitions.
A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯ lies.
This statement is also true. A 95% confidence interval for the sample mean x¯ means that if we were to take multiple samples of the same size from the same population and calculate the sample mean x¯ and the corresponding 95% confidence interval for each sample, then 95% of those intervals would contain the true population mean μ.
The true mean μ is always inside the corresponding confidence interval.
This statement is false. While it is true that the true population mean μ is expected to be inside the confidence interval in most cases, it is not guaranteed to be inside the interval for any particular sample or experiment.
For a sample size n=29, the number of degrees of freedom is n1=28.
This statement is true. The number of degrees of freedom for a t-distribution is equal to n1, where n is the sample size.
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not contain the true mean μ.
This statement is also true. The 95% confidence level means that in the long run, 95% of the intervals will contain the true population mean μ, and approximately 5% will not. Therefore, if we construct 100 confidence intervals, we would expect approximately 5 of them to not contain the true population mean μ.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?