Question

For each problem, a) attach StatCrunch output, b) write a sentence of interpretation, and c) state the interval in margin of error form. 2. In a sample of 200 people, 112 said they always recycle. Calculate and interpret a 95% confidence interval for the proportion of all people who always recycle.

Answer 1

Solution:

Part a

StatCrunch output:

Part b

We are 95% confident that the population proportion of the people who always recycle will be lies within 49.12% and 62.88%.

Part c

Confidence interval for Population Proportion is given as below:

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

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

We are given

Sample size = n = 200

Number of successes = x = 112

Confidence level = 95%

Critical Z value = 1.96

P = x/n = 112/200 = 0.56

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

Confidence Interval = 0.56 ± 1.96* sqrt(0.56*(1 – 0.56)/200)

Confidence Interval = 0.56 ± 1.96* 0.0351

Confidence Interval = 0.56 ± 0.0688

Lower limit = 0.56 - 0.0688 = 0.4912

Upper limit = 0.56 + 0.0688 = 0.6288

Confidence Interval = 0.56 ± 0.0688