Q.22 - The Practice of Statistics for AP

Question

Your teacher prepares a large container full of colored beads. She claims that $1/8$ of the beads are red, $1/4$ are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim. The smallest number of beads you can take so that the conditions for performing inference are met is

 (a) 15.  (c) 30. (e) 80. 

 (b) 16. (d) 40 

Step-by-Step Solution

Answer

The correct option is $\left(d\right) 40$

Step 1: Given information

Given in the question that,  Your teacher prepares a large container full of colored beads. She claims that  of$1/8$ the beads are red, $1/4$ are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim .

Step 2: Explanation

The table is,

Quadrant	Frequency
$1$	$18$
$2$	$22$
$3$	$39$
$4$	$21$

The proportions are$\frac{1}{8},\frac{1}{4},\frac{5}{8}$

Here, the smallest probability is $1 / 8$, thus it would be used to compute the frequency.

The expected frequencies are calcualted as:

$E=n{p}_1=15\left(\frac{1}{8}\right)=1.875$

$E=np1=16\left(\frac{1}{8}\right)=2$

$E=n{p}_1=30\left(\frac{1}{8}\right)=3.75$

$E=n{p}_1=40\left(\frac{1}{8}\right)=5$

$E=n{p}_1=80\left(\frac{1}{8}\right)=10$

Here, conditions are fulfilling for (d) and (e) but the smallest sample size is contained by (d). Thus, the correct option is (d).