### Constructing a Confidence IntervalTo construct the indicated confidence interval for the population mean \( \mu \) using the t-distribution, follow these parameters and assumptions:**Parameters:**- Confidence level (\( c \)): 0.95- Sample mean (\( \bar{x} \)): 14.1- Sample standard deviation (\( s \)): 4.0- Sample size (\( n \)): 7**Assumptions:**- The population is normally distributed.**Instructions:**1. Use the confidence interval formula for the mean with the t-distribution: \[ \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right) \] where \( t^* \) is the t-score for the desired confidence level and degrees of freedom (\( n-1 \)).2. Calculate the degrees of freedom: \[ df = n - 1 = 6 \]3. Look up the t-score for a 95% confidence level with 6 degrees of freedom.4. Compute the margin of error: \[ ME = t^* \left(\frac{s}{\sqrt{n}}\right) \]5. Calculate the confidence interval: \[ \left(\bar{x} - ME, \bar{x} + ME\right) \]**Answer:**Enter your computed confidence interval in the fields provided and click "Check Answer."**Note:**Round your final results to one decimal place as needed.

Name: ### Constructing a Confidence IntervalTo construct the indicated conf
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Description: ### Constructing a Confidence IntervalTo construct the indicated confidence interval for the population mean \( \mu \) using the t-distribution, follow these parameters and assumptions:**Parameters:**- Confidence level (\( c \)): 0.95- Sample mean (

Given: c=0.95x¯=14.1s=5n=7Here, sample standard deviation is known, thus, t-confidence interval is to be computed. The degree of freedom is: Df = n-1 = 7-1 = 6 The critical value is: tα/2,df=t0.05/2,6=2.447 The confidence interval is computed as: CI=x¯±tα/2,df×sn=14.1±2.447×47=(10.4,17.8) Thus, the confidence interval is (10.4, 17.8).

Math

Statistics

Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.95, x=14.1, s=4.0, n=7 (Round to one decimal place as needed.)

Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed. c= 0.95, x=14.1, s=4.0, n=7 (Round to one decimal place as needed.)

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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