6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion

Using a CI to Assess a Claim

A confidence interval gives a range of plausible values for a parameter. We can use it to assess whether a specific value of the parameter is plausible.

Logic:

Example: A company claims that 70% of its customers are satisfied. A survey of 200 customers finds ${\hat{p} = 0.64}$.

Construct a 95% CI: ${0.64 \pm 1.96\sqrt{0.64(0.36)/200} = 0.64 \pm 0.066 = (0.574, 0.706)}$

Since 0.70 is inside the interval, the company's claim of 70% satisfaction is plausible.

But 0.80 is outside the interval — a claim of 80% satisfaction would not be plausible.