7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.
A) $6.0

Question

7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight. 
A) $6.0 < \mu < 11.4$
B) $7.7 < \mu < 9.7$
C) $8.3 < \mu < 9.1$
D) $7.9 < \mu < 9.5$

Quizplus · Accepted Answer

To find the 95% confidence interval for the true mean weight of the squirrels, we use the formula for the confidence interval of the mean with a t-distribution (since the sample size is small and the population standard deviation is unknown): $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the t-score for 95% confidence and $n-1$ degrees of freedom, $s$ is the sample standard deviation, and $n$ is the sample size.Given: $\bar{x} = 8.7$, $s = 1.1$, and $n = 7$.Degrees of freedom $df = n - 1 = 6$.For a 95% confidence interval and 6 degrees of freedom, the t-score (from a t-table or calculator) is approximately 2.447.Plugging these values into the formula gives us the margin of error: $E = 2.447 \cdot \frac{1.1}{\sqrt{7}} \approx 1.0$.Thus, the confidence interval is $8.7 \pm 1.0$, which is $7.7 < \mu < 9.7$.

7 Squirrels Were Found to Have an Average Weight of 8.7