Question

The population proportion of success is 60% and the intended sample size is n = 229. Before drawing a sample from the population, you first want to estimate the interval in which the middle-most 80% of the sample proportions would fall. Give answers in decimal format (as opposed to fractions or percentages). Interval for middle-most 80% of sample proportions:

Answer 1

Solution:

GIven:

Population proportion = = 0.60

P

Sample size = n = 229

Confidence level = 0.80

So, level of significance = α=0.2

Zc = 1.282 ...Using excel formula, =ABS(NORMSINV(0.2/2))

Therefore, 80% confidence interval for sample proportion is,

p(1-P) p(1-P) P - ze P + zc1 n 0.6 - 1.282 x 0.6(1 -0.6) ,0.6 + 1.282 x 229 0.6(1 -0.6) 229 (0.559, 0.641)

Hence, interval for middle most 80% of sample proportion = (0.559 , 0.641)

Done