Use the sample mean $2.4$ and the margin of error $0.3$ to form a low and a high estimate. What do you get when you do $2.4 - 0.3$ and $2.4 + 0.3$?

Once you have the two numbers from the previous hint, look for the choice whose inequality has $\mu$ strictly between those two numbers.

In the Desmos expression list, type 2.4-0.3 on one line and 2.4+0.3 on another line. Note the two numeric results; these are the lower and upper plausible values for the mean based on the margin of error.

Look at the two values Desmos gives you, and then compare them with the answer options. Identify the option whose inequality has $\mu$ strictly between those two values.

The symbol $\mu$ stands for the true mean homework time (in hours) for all high school students in the district.

We are told:

• Sample size: $200$ students (random sample)
• Sample mean: $2.4$ hours
• Margin of error: $0.3$ hour

We need to decide which statement about the true mean $\mu$ is most reasonable, based on the sample mean and margin of error.

A margin of error of $0.3$ hour means the true mean $\mu$ is expected to be within $0.3$ hour above or below the sample mean $2.4$.

So we make an interval by doing:

• Lower end: sample mean $-$ margin of error
• Upper end: sample mean $+$ margin of error

Compute the two endpoints using the sample mean $2.4$ and margin of error $0.3$:

• Lower endpoint: $2.4 - 0.3 = 2.1$
• Upper endpoint: $2.4 + 0.3 = 2.7$

So the plausible range for the true mean is between $2.1$ and $2.7$ hours.

We want the choice that says the true mean $\mu$ is between $2.1$ and $2.7$.

Written as an inequality, that is:

This matches answer choice C.