Final answer:
The value of the test statistic is z = 1.20, calculated using the z-score formula and the given population standard deviation, sample mean, and sample size. Therefore, the correct value of the test statistic is z = 1.20, which corresponds to option C.
Step-by-step explanation:
To calculate the value of the test statistic for a hypothesis test regarding the mean lifespan of wombats, we use the formula for the z-score:
\[ z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})} \]
where \( \bar{x} \) is the sample mean, \( \mu \) is the population mean, \( \sigma \) is the population standard deviation, and \( n \) is the sample size.
In this case:
- \( \bar{x} = 17.1 \) years (sample mean)
- \( \mu = 16 \) years (assumed population mean)
- \( \sigma = 6 \) years (population standard deviation)
- \( n = 43 \) (sample size)
Let's calculate the z-score:
\[ z = \frac{17.1 - 16}{(6/\sqrt{43})} \]
\[ z = \frac{1.1}{(6/\sqrt{43})} \]
\[ z = \frac{1.1}{0.914} \]
\[ z = 1.20 \]
Therefore, the correct value of the test statistic is z = 1.20, which corresponds to option C.