In a survey, the planning value for the population proportion is p * = 0.26. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)

n = 296

Sample size n = 296

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√ (p (1-p) / n)

x+/-M. E

M. E = z√ (p (1-p) / n)

Making n the subject of formula;

n = (p (1-p) / (M. E/z) ^2) ... 1

Given that;

Proportion p = 0.26

Number of samples n = ?

Confidence interval = 95%

z (at 95% confidence) = 1.96

Substituting the values into equation 1;

n = (0.26 (1-0.26)) / ((0.05/1.96) ^2)

n = 295.649536

n = 296

Sample size n = 296