**Constructing a Confidence Interval for the Population Mean**To construct the indicated confidence interval for the population mean $\mu$ using the t-distribution, assume the population is normally distributed. The given data is as follows:- Confidence level ($c$): 0.95- Sample mean ($\bar{x}$): 12.1- Sample standard deviation ($s$): 0.71- Sample size ($n$): 14The goal is to determine the confidence interval and present the values within brackets as $(\ ,\ )$.*Note: Round to one decimal place as needed.*

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Description: **Constructing a Confidence Interval for the Population Mean**To construct the indicated confidence interval for the population mean $\mu$ using the t-distribution, assume the population is normally distributed. The given data is as follows:- Conf

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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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**Constructing a Confidence Interval for the Population Mean**

To construct the indicated confidence interval for the population mean $\mu$ using the t-distribution, assume the population is normally distributed. The given data is as follows:

- Confidence level ($c$): 0.95
- Sample mean ($\bar{x}$): 12.1
- Sample standard deviation ($s$): 0.71
- Sample size ($n$): 14

The goal is to determine the confidence interval and present the values within brackets as $(\ ,\ )$.

*Note: Round to one decimal place as needed.*

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathrm{\mathbf{given}:}$

$\mathrm{Confidence\;level\;(C)=0.95\;or\;95\%}$

$\mathrm{Sample\;mean\;(\bar x)=12.1}$

$\mathrm{Sample\;standard\;deviation\;(s)=0.71}$

$\mathrm{Sample\;size\;(n)=14}$

Since population standard deviation is unknown, Use t-distribution to find t-critical value.

Find the t-critical value:

$\mathbf{Degrees\;of\;freedom\;(df)}=n-1=14-1=\mathbf{13}$

Refer t-distribution table and look for t value corresponding to degrees of freedom=13 & confidence level of 95% for the two-tail test.

Therefore,

$\mathbf{t_{\frac{\alpha }{2}}=2.160}$

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