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Q. 10

Expert-verified

The Practice of Statistics for AP

Found in: Page 797

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

We record data on the population of a particular country from $1960$ to $2010$ . A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is,
log ( population) $= - 13.5 + 0.01$ (years).
Based on this equation, the population of the country in the year 2020 should be about
(a) $6.7$
(b) $812$
(c) $5, 000, 000$
(d) $6, 700, 000$
(e) $8, 120, 000$ .

The population of the country in the 2020 should be about $5, 000, 000$ . The correct option is (c).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

The population of the country in the year 2020 should be about log (population) $= - 13.5 + 0.01$ .

Step 2: Explanation

Putting the year with 2020 :

log (population) $= - 13.5 + 0.01 (2020)$

$= 6.7$

Taking the exponential

Population $= 10^{6.7}$

Evaluate $= 5011872$

$= 5000000$

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