**Constructing a Confidence Interval for a Population Mean**When given the task to construct a confidence interval for the population mean \(\mu\) using the t-distribution, it's essential to assume the population is normally distributed. Here's how to construct a 99% confidence interval with the given data:### Given Values:- Confidence level (\(c\)): 0.99- Sample mean (\(\bar{x}\)): 13.8- Sample standard deviation (\(s\)): 4.0- Sample size (\(n\)): 7### Objective:To find the 99% confidence interval using a t-distribution.### Steps to Construct the Interval:1. **Identify the t-score:** - Use a t-distribution table or calculator to find the t-score that corresponds to a 99% confidence level with \(n-1\) degrees of freedom (in this case, 6 degrees of freedom).2. **Calculate the Standard Error (SE):** \[ SE = \frac{s}{\sqrt{n}} = \frac{4.0}{\sqrt{7}} \]3. **Construct the Confidence Interval:** \[ \text{Confidence Interval} = \bar{x} \pm (t \times SE) \] Where \(t\) is the t-score obtained from the t-distribution.4. **Round to One Decimal Place:** - Ensure the final confidence interval is rounded to one decimal place as specified.The final confidence interval will look like \(( \_\_.\_ , \_\_.\_ )\), providing a range within which the population mean is likely to fall with 99% confidence.### Note:- It is critical to use the appropriate t-score and SE to ensure accuracy.- Computers or statistical software can help automate these calculations and minimize errors.

Given: n= 7.0 , x̄= 13.8 s= 4.0 degree of freedom=n-1= 6.0 At 99.0 % confidence level with d.o.f.=…

Answered: Construct the indicated confidence…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.99, x 13.8, s=4.0, n=7 The 99% confidence interval using a t-distribution is (OD. (Round to one decimal place as needed.)