Answer
Yes.
Work Step by Step
A big confidence interval can be used if the number of successes and failures is both at least $10$ of both samples. Thus here we can use a big confidence interval.
The Basic Practice of Statistics 7th Edition
by Moore, David S.; Notz, William I.; Fligner, Michael A.
Published by
W. H. Freeman
ISBN 10:
146414253X
ISBN 13:
978-1-46414-253-6
Chapter 23 - Comparing Two Proportions - Chapter 23 Exercises - Page 553: 23.17a
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