Question

3) A company says that its product has a 95% positive approval rating. A polling company found that 89% of 500 people surveyed approved of the product. Construct a 90% proportion confidence interval based on this data and determine whether the data supports the 95% positive approval rating claim.

Start by using the binomial distribution (p ̂ + q ̂)n = 1, and x ̅ = np ̂.

Use Summary 5b, Table 1, Column 3.

What is n?

What is p ̂?

What is q ̂?

What is x ̅?

What is p? (Note: p is based on our belief about the population. p ̂ is based on the sample.)

Let σp = sqrt((p ̂q ̂)/n). What is σp ?

We want to make a confidence interval by using the formula

z = k/σp

Should we use a 1 tail or 2 tail z-score?

What value of z corresponds to the 90% confidence interval?

What is k?

Construct the confidence interval

(p ̂ – k) < ptrue < (p ̂ + k)

Is your confidence interval consistent with the belief that 95% approval rating claim? (yes or no, and explain your answer using your computed confidence interval).

Answer 1