Which of the following best explains why the t-test for a population mean $\mu$ is considered robust, while the chi-square test for a population standard deviation $\sigma$ is not?

A meal delivery company had a standard deviation of $2.5$ minutes in delivery times under its old logistics system. After switching to a new route optimization algorithm, the company recorded the following delivery times (in minutes) for a simple random sample of $12$ deliveries:

$31.2,30.9,32.1,29.8,31.5,30.2,32.7,31.0,30.6,31.9,30.7,31.3$

At the $0.05$ significance level, test the claim that the new system results in less variation in delivery times than the old system (i.e., the standard deviation is less than $2.5$ minutes).

A researcher collects a simple random sample of cholesterol levels from $25$ adult men and finds the sample standard deviation is $18.7$ $\text{mg/dL}$. Test, at the $0.01$ significance level, the claim that the standard deviation of cholesterol levels in adult men is the same as the known standard deviation for adult women, which is $15.2$ $\text{mg/dL}$.

A manufacturing company is evaluating the consistency in the weight of metal washers produced during a recent upgrade to their production line. The company claims that the variability in washer weight is less than $0.07000\text{ g}$. After analyzing a sample, the test yields a $p$-value of $0.0027$. What conclusion can be drawn regarding the null hypothesis? Does the evidence support the company’s claim? What do the results indicate about the new production system?