The 99% confidence interval to estimate the mean number of hours per week people watch Netflix is (20.5, 24.3). What value must be in the interval?

To find the value that must be in the given confidence interval of (20.5, 24.3), we need to determine the range of values that the mean number of hours per week people watch Netflix could take to maintain a 99% confidence.

1. Break Down the Problem

• The confidence interval is given as (20.5, 24.3).
• We need to identify a value that lies within this interval.

2. Relevant Concepts

• A confidence interval gives a range of plausible values for a population parameter (in this case, the mean) based on a sample statistic.
• A value that must be in the interval is any number that is greater than or equal to 20.5 and less than or equal to 24.3.

3. Analysis and Detail

• The lower bound of the interval is 20.5.
• The upper bound of the interval is 24.3.
• Therefore, any value $x$ such that $20.5 \leq x \leq 24.3$ will satisfy this condition.
• For example, we could choose the midpoint of the interval as a representative value: $\text{Midpoint} = \frac{20.5 + 24.3}{2} = \frac{44.8}{2} = 22.4$

4. Verify and Summarize

• Both endpoints (20.5 and 24.3) are included in the interval.
• Therefore, any value between or equal to these numbers, such as 22.4, is valid.

Final Answer

The value that must be in the interval (20.5, 24.3) is any number within the range, for example, 22.4.