A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and standard deviation of 1.88 gm. Assuming these squirrels can be considered a random sample of all red squirrels which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels?
A) $ 12.32 \pm 2.228\left(\frac{1.88}{\sqrt{9}}\right) $

B) $ 12.32 \pm 2.228\left(\frac{1.88}{\sqrt{10}}\right) $

C) $ 12.32 \pm 2.262\left(\frac{1.88}{\sqrt{10}}\right) $

D) $ 12.32 \pm 1.96\left(\frac{1.88}{\sqrt{10}}\right) $

E) $ 12.32 \pm 2.268\left(\frac{1.88}{\sqrt{9}}\right) $

Question

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 grams and standard deviation of 1.88 gm. Assuming these squirrels can be considered a random sample of all red squirrels which of the following formulas gives a 95% confidence interval for the mean weight of all squirrels? 
A) $ 12.32 \pm 2.228\left(\frac{1.88}{\sqrt{9}}\right) $

B) $ 12.32 \pm 2.228\left(\frac{1.88}{\sqrt{10}}\right) $

C) $ 12.32 \pm 2.262\left(\frac{1.88}{\sqrt{10}}\right) $

D) $ 12.32 \pm 1.96\left(\frac{1.88}{\sqrt{10}}\right) $

E) $ 12.32 \pm 2.268\left(\frac{1.88}{\sqrt{9}}\right) $

Quizplus · Accepted Answer

To find a 95% confidence interval for the mean weight of all red squirrels, we use the formula:

$$	ext{CI} = \bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

where $\bar{x}$ is the sample mean (12.32 grams), $s$ is the sample standard deviation (1.88 grams), $n$ is the sample size (10 squirrels), and $t^*$ is the t-score that corresponds to a 95% confidence level with $n-1$ degrees of freedom.

Using a t-table with 9 degrees of freedom (since we're using a sample size of 10, which means $n-1=9$ degrees of freedom), we find that $t^* = 2.262$.

Therefore, the 95% confidence interval for the mean weight of all red squirrels is:

$$	ext{CI} = 12.32 \pm 2.262\left(\frac{1.88}{\sqrt{10}}ight)$$

which simplifies to:

$$	ext{CI} = (11.30, 13.34)$$

Therefore, the best choice is C.

A Wildlife Biologist Wants to Determine the Mean Weight of Adult