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At a primate reserve, the mean age of all the male primates is $15$ years, and the mean age of all female primates is $19$ years. Which of the following must be true about the mean age $m$ of the combined group of male and female primates at the primate reserve? $\newline$ A) $m = 17$ $\newline$ B) m > 17 $\newline$ C) m < 17 $\newline$ D) 15 < m < 19

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Interpret confidence intervals for population means

Full solution

Q. At a primate reserve, the mean age of all the male primates is

15

years, and the mean age of all female primates is

19

years. Which of the following must be true about the mean age

m

of the combined group of male and female primates at the primate reserve?

\newline

A)

m = 17

\newline

B)

m > 17

\newline

C)

m < 17

\newline

D)

15 < m < 19

Understand the problem: Step $1$ : Understand the problem. We know the mean age of male primates is $15$ years and for female primates, it's $19$ years. We need to find the range or exact value of the mean age $m$ for the combined group.
Analyze the options: Step $2$ : Analyze the options. We have four choices: $\newline$ A) $m = 17$ $\newline$ B) m > 17 $\newline$ C) m < 17 $\newline$ D) 15 < m < 19 $\newline$ We need to determine which of these statements must be true based on the given mean ages.
Consider the weighted mean: Step $3$ : Consider the weighted mean. The actual mean $m$ of the combined group depends on the number of males and females. If there are more females, the mean will be closer to $19$ ; if more males, closer to $15$ . Without knowing the exact numbers, we can't calculate $m$ exactly, but we know it must be between $15$ and $19$ .
Eliminate incorrect options: Step $4$ : Eliminate incorrect options. Since $m$ must be between $15$ and $19$ , options A) $m = 17$ and B) m > 17 can't always be true. Option C) m < 17 also can't always be true because $m$ could be closer to $19$ if there are significantly more females.
Confirm the correct answer: Step $5$ : Confirm the correct answer. The only option that must be true, given that $m$ will vary between $15$ and $19$ depending on the population distribution, is D) 15 < m < 19 .

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