1. The problem is to recalculate the test statistic correctly when the previous calculation was wrong. 2. The test statistic formula depends on the type of test (e.g., z-test, t-test). For a one-sample z-test, the formula is: $$z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$$ where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. 3. Important rules: - Use the correct values for $\bar{x}$, $\mu_0$, $\sigma$, and $n$. - Ensure the standard deviation and sample size are correctly plugged in. 4. Suppose the previous test statistic was calculated with wrong $\bar{x}$ or $\sigma$. Recalculate using the correct values. 5. Example: If $\bar{x} = 105$, $\mu_0 = 100$, $\sigma = 15$, and $n = 25$, then: $$z = \frac{105 - 100}{\frac{15}{\sqrt{25}}} = \frac{5}{\frac{15}{5}} = \frac{5}{3}$$ 6. Show intermediate cancellation: $$z = \frac{5}{\cancel{\frac{15}{5}}} = \frac{5}{3}$$ 7. Final answer: $$z = 1.67$$ This is the correctly recalculated test statistic.