Confidence Interval Estimate

Question

In a Harris poll of 2000 human resource professionals, 41.8% said that body piercings and tattoos were big grooming red flags. Construct a 95% confidence interval estimate for the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags and write a statement that correctly interprets the confidence interval that you constructed.

Answer 1

Relevant formulas:

Confidence Interval = p ± Zcrit×(sqrt (pq/n))

Population proportion (p) = X/N

q = 1 - p

Margin of Error (E) = Zcrit×(sqrt (pq/n))

Step 1: State Your Givens

n = 2000

p = 0.418

q = 0.582 (**We got this answer by taking 1 - 0.418.**)

Z_α/2=Z_0.025=1.96

Step 2: Calculate Margin of Error with Given Information

Margin of Error (E) = Zcrit×(sqrt (pq/n))

=1.96 × sq rt ((.418)(.582)/2000)

=0.0216

Step 3: Calculate Confidence Interval

A 95% confidence interval for the population proportion (p) is,

p-E < p < p+E

.418 - 0.0216 < p < .418 + 0.0216

0.3964 < p < 0.4396

Step 4: Interpret Your Results

We are 95% confident that the proportion of all human resource professionals that believe that body piercings and tattoos are big grooming red flags are 39.64% and 43.96%