# Estimating a Population Mean## Sample DataYou intend to estimate a population mean $ \mu $ with the following sample:- 30.5- 18.4- 39.1- -7.6- 14.7- 27.8- 9.6- 1.7## TaskYou believe the population is normally distributed. Find the 90% confidence interval. Enter your answer as an **open-interval** (i.e., in parentheses), accurate to two decimal places (because the sample data are reported accurate to one decimal place).### Calculation Step90% C.I.: __________*Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.***Question Help:** [

Name: # Estimating a Population Mean## Sample DataYou intend to estimate a
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Description: # Estimating a Population Mean## Sample DataYou intend to estimate a population mean $ \mu $ with the following sample:- 30.5- 18.4- 39.1- -7.6- 14.7- 27.8- 9.6- 1.7## TaskYou believe the population is normally distributed. Find the 90% confidence

From the provided data we have, Mean =x¯ =∑ixin…

Answered: You intend to estimate a population…

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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# Estimating a Population Mean

## Sample Data

You intend to estimate a population mean $ \mu $ with the following sample:

- 30.5
- 18.4
- 39.1
- -7.6
- 14.7
- 27.8
- 9.6
- 1.7

## Task

You believe the population is normally distributed. Find the 90% confidence interval. Enter your answer as an **open-interval** (i.e., in parentheses), accurate to two decimal places (because the sample data are reported accurate to one decimal place).

### Calculation Step

90% C.I.: __________

*Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.*

**Question Help:** [

Expert Solution

Step 1

From the provided data we have,

$M e a n = \bar{x} = \sum_{i} \frac{x_{i}}{n} = \frac{30.5 + 18.4 + 39.1 - 7.6 + 14.7 + 27.8 + 9.6 + 1.7}{8} = \frac{134.2}{8} = 16.775$

$S a m p l e s \tan d a r d d e v i a t i o n = s = \sqrt{\frac{\sum_{i} {(x_{i} - \bar{x})}^{2}}{n - 1}} = \sqrt{\frac{{(30.5 - 16.775)}^{2} + (18.4 - 16.775)^{2} + (39.1 - 16.775)^{2} (- 7.6 - 16.775)^{2} + . . . . . .}{8 - 1}} = \sqrt{241.165} = 15.52949$

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