Question

3. Suppose the mystery bag had resulted in the following number of red chips. Using the simulated sampling distributions found earlier in this lesson, find a margin of error in each case.
a. The number of red chips in a random sample of size 30 was 10.
b. The number of red chips in a random sample of size 30 was 21.
c. The number of red chips in a random sample of size 50 was 22.

Answer 1

Answer:

a) 0.172

b) 0.167

c) 0.1404

Step-by-step explanation:

Margin of error, E = $2\times\sqrt{\frac{p(1-p)}{n}}$

here,

p = probability of the event

n = sample size

a) n = 30

p = 10 ÷ 30 = 0.333

Therefore,

E = $2\times\sqrt{\frac{0.333(1-0.333)}{30}}$

= 2 × 0.0861

= 0.172

b)  n = 30

p = 21 ÷ 30 = 0.7

Therefore,

E = $2\times\sqrt{\frac{0.7(1-0.7)}{30}}$

= 2 × 0.0836

= 0.167

c) n = 30

p = 22 ÷ 50 = 0.44

Therefore,

E = $2\times\sqrt{\frac{0.44(1-0.44)}{50}}$

= 2 × 0.0702

= 0.1404