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Chapter 10: Q.1.1 (page 608)

Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag 1has 25%red crackers and Bag 2has 35%red crackers. Each bag contains more than 500crackers. Using a paper cup, your teacher takes an SRS of 50crackers from Bag 1 and a separate SRS of 40crackers from Bag 2. Let p1^-p2^be the difference in the sample proportions of red crackers.

What is the shape of the sampling distribution ofp1^-p2^ ? Why?

Short Answer

Expert verified

It is approximately normally distributed.

Step by step solution

01

Given Information

The proportion of red crackers in Bag1p1=25%

=0.25.

The proportion of red crackers in Bag 2p2=35%

=0.35.

Number of crackers in Bag 1n1=50.

Number of crackers in Bag 2n2=40.

02

Explanation

The required conditions could be checked as:

n1p1=50(0.25)

=12.5>10

n11-p1=50(1-0.25)>10

localid="1650365073121" n2p2=40(0.35)

=14>10

localid="1650365094942" n21-p2=40(1-0.65)

=26>10

Since all the values are greater than 10. Thus, it could be said that distribution is approximately normally distributed.

03

Final Answer

It is approximately normally distributed.

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