Answered: sample of size 1045 with a mean of 33.5…

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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Assume that a sample is used to estimate a population mean μμ. Find the 99.9% confidence interval for a sample of size 1045 with a mean of 33.5 and a standard deviation of 13.5.

Assume that a sample is used to estimate a population mean $ \mu $. Find the 99.9% confidence interval for a sample of size 1045 with a mean of 33.5 and a standard deviation of 13.5. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

\[ \text{[ ]} < \mu < \text{[ ]} \]

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

Expert Solution

Step 1

As the population standard deviation is not known, we will use t-distribution.

Given:

$X ˉ = 33.5$

$s = 13.5$ .

$n = 1045$

Confidence level is= 99.9%

The number of degrees of freedom will be

$d f = 1045 - 1 = 1044$

The significance level will be,

$α = 0.00099999999999989$ .

Based on the provided information, the critical t-value for $α = 0.001$ and $d f = 1044$ degrees of freedom is 3.29987, i.e., $3 . 300 (rounded to three decimal places)$ .

The 99.9% confidence can be calculated as:

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