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Q.1.1

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The Practice of Statistics for AP
Found in: Page 501
The Practice of Statistics for AP

The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

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Short Answer

To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002 gram. How many measurements must be averaged to get a margin of error of 0.0001 with 98% confidence? Show your work.

The required number is 22 .

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given information 

Given in the question that, To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002 gram . We need to find that how many measurements must be averaged to get a margin of error of 0.0001 with 98% confidence.

Step 2: Explanation

Population standard deviation (σ)=0.0002

Margin of error (E)=0.0001

Confidence level =98%

The formula to compute the sample size is:

n=zα/2×σE2

The z-score at 99%confidence level is calculated from the standard normal table like this,

za/2=z0.02/2

=2.33

The number of measurements is calculated as:

n=zα/2×σE2

=2.33×0.00020.00012

=21.648

≈22

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