Question

Crest toothpaste is reviewing plans for its annual survey of toothpaste purchasers. With the following two cases, calculate the sample size pertaining to the key variable under consideration. Where information is missing, provide reasonable assumptions.

Answer 1

At the 95% confidence level the confidence interval for this proportion is:

0.5 = 1.96( √0.21 / n)

0.5 / 1.96 = √(0.21 / n)

0.3 x √n = √0.21

√n = √( 0.21 / 0.3)

= √0.7

n = 0.83

Explanation:

Solution:

Case 1:

Acceptable error = precision = 4%

Share last year = p = 23% = 0.23

q = 1 – p = 1 – 0.23

q = 0.77

Standard error/ of proportion = √pq/n

= √(0.23(0.77) )/ n

= √0.1771 / n

For a 95% confidence level = z = 1.96

At the 95% confidence level the confidence interval for this proportion is:

0.4 = 1.96( √0.1771 / n)

0.4 / 1.96 = √0.1771 / n

0.2 x √n = √0.1771

√n = √ 0.1771 / 0.2

n = 443

case 2 :

Acceptable error = precision = 5%

Switched last year = p = 30% = 0.30

q = 1 –p = 1 – 0.3 = 0.7

Standard error/ of proportion = √pq/n

= √(0.3(0.7) )/ n

= √0.21 / n

For a 95% confidence level = z = 1.96

At the 95% confidence level the confidence interval for this proportion is:

0.5 = 1.96( √0.21 / n)

0.5 / 1.96 = √(0.21 / n)

0.3 x √n = √0.21

√n = √( 0.21 / 0.3)

= √0.7

n = 0.83