Question

A December Galllup Poll found that 38% of recent college graduates "strongly agreed" that college was worth the cost. The random sample was based on 1025 recent college graduates.

a) Find a 90% confidence interval for the percentage of all recent college graduates who strongly agree that college was worth the cost.

b) Interpret the interval in context by completing the sentence: "I am 90% confident that..."

Answer 1

Part a

Confidence interval for Population Proportion is given as below:

Confidence Interval = p̂ ± Z* sqrt(p̂*(1 – p̂)/n)

Where, p̂ is the sample proportion, Z is critical value, and n is sample size.

We are given

Sample size = n = 1025

Sample proportion = p̂ = 0.38

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence Interval = p̂ ± Z* sqrt(p̂*(1 – p̂)/n)

Confidence Interval = 0.38 ± 1.6449* sqrt(0.38*(1 – 0.38)/n)

Confidence Interval = 0.38 ± 1.6449* 0.0152

Confidence Interval = 0.38 ± 0.0249

Lower limit = 0.38 - 0.0249 = 0.3551

Upper limit = 0.38 + 0.0249 = 0.4049

Confidence interval = (0.3551, 0.4049)

Confidence interval = (35.51%, 40.49%)

Part b

I am 90% confident that the population percentage of all recent college graduates who strongly agree that college was worth the cost will lies between 35.51% and 40.49%.