### Constructing a 98% Confidence IntervalGiven the following data:- Sample size (\(n\)) = 19- Sample mean (\(\overline{x}\)) = 32- Sample standard deviation (\(s\)) = 11We are tasked with constructing a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population.#### Steps to Construct the Confidence Interval1. **Identify the sample size (\(n\)), sample mean (\(\overline{x}\)), and sample standard deviation (\(s\))**: - \(n = 19\) - \(\overline{x} = 32\) - \(s = 11\)2. **Determine the appropriate t-score for a 98% confidence level**: - Degrees of freedom (\(df\)) = \(n - 1 = 19 - 1 = 18\) - Using a t-distribution table or calculator, find the t-score for 98% confidence level with \(df = 18\). The value is approximately \(t \approx 2.552\).3. **Calculate the standard error of the mean (SEM)**: \[ \text{SEM} = \frac{s}{\sqrt{n}} = \frac{11}{\sqrt{19}} \approx 2.524 \]4. **Compute the margin of error (ME)**: \[ \text{ME} = t \times \text{SEM} = 2.552 \times 2.524 \approx 6.4 \]5. **Determine the confidence interval**: - Lower limit: \(\overline{x} - \text{ME} = 32 - 6.4 = 25.6\) - Upper limit: \(\overline{x} + \text{ME} = 32 + 6.4 = 38.4\)So, the 98% confidence interval for the population mean is:\[25.6 < \mu < 38.4\]#### Summary:Fill in the results in the boxes provided:\[\boxed{25.6} < \mu < \boxed{38.4}\]

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Description: ### Constructing a 98% Confidence IntervalGiven the following data:- Sample size (\(n\)) = 19- Sample mean (\(\overline{x}\)) = 32- Sample standard deviation (\(s\)) = 11We are tasked with constructing a confidence interval at a 98% confidence level

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Answered: If n=19, (x-bar)=32, and s=11,…

Math

Statistics

If n=19, (x-bar)=32, and s=11, construct a confidence interval at a 98% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place.

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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