he population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?

z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576

Use the table above for the z-score, and be sure to round up to the nearest integer.

Expert Solution
Step 1

Given : 

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. There is 95% confident that the sample mean is within 2 inches of the true population mean .  

       Standard deviation : σ=3.7 inches  , Margin of error : E = 2 inches

At 95% confidence level : 

α refers to the likelihood that the true population parameter lies outside the confidence interval . It is usually expressed as a proportion. Thus, if the confidence level is 95%, then alpha would equal 1 - 0.95 or 0.05. 

                    α = 0.05 

 

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