7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval

Using a t CI to Assess Claims

A t confidence interval gives a range of plausible values for ${\mu}$. If a claimed mean ${\mu_0}$ falls outside the CI, the claim is not plausible at the corresponding significance level.

Example: A manufacturer claims their batteries last an average of 100 hours. A sample of 20 batteries has ${\bar{x} = 95.3}$ hours and ${s = 8.2}$ hours.

Since 100 is outside the interval, we have convincing evidence that the true mean battery life is less than the claimed 100 hours.