Question

The sodium content in the soda water of two different brands has been compared. The study provided the summary information shown below for bottles containing 750 millilitres of soda water. How many of these bottles of each brand would need to be sampled in order to estimate the difference in the mean sodium content to within 0.5 with​ 95% reliability?

Brand A Brand B

Sample size 25 20

Mean 148 152

Variance 2.2 2.5

a) n1=n2=37

b) n1=n2=26

c) n1=n2=171

d) n1=n2=73

Answer 1

Answer: The sodium content in the soda water of two different brands has been compared. The study provided the summary information shown below for bottles containing 750 millilitres of soda water. How many of these bottles of each brand would need to be sampled in order to estimate the difference in the mean sodium content to within 0.5 with​ 95% reliability?

Solution:

For Brand A:

At 95% confidence interval,

Zα/2 = 1.96

Margin of error E = 0.5

Sample size n:

n = (Zα/2 / E)^2 * variance

n = (1.96 / 0.5)^2 * 2.2

n = 33.8061

n = 34

Therefore required sample size is 34.

For Brand B:

At 95% confidence interval,

Zα/2 = 1.96

Margin of error E = 0.5

Sample size n:

n = (Zα/2 / E)^2 * variance

n = (1.96 / 0.5)^2 * 2.5

n = 38.416

n = 38

Therefore required sample size is 38.

n1 + n2 = 34 + 38

n1 = n2 = 72

Therefore, option d) is approximately correct answer.