Final answer:
To find the 95% confidence interval for the true mean weight of the squirrels, use the sample mean, standard deviation, and sample size to calculate the standard error and apply the t-distribution formula to estimate the interval.
Step-by-step explanation:
To answer the question regarding the 95% confidence interval for the true mean weight of squirrels, we employ the t-distribution because the sample size is small (n < 30) and the population standard deviation is unknown.
We have a sample mean (μ) of 8.7 ounces, a sample standard deviation (s) of 1.1 ounces, and a sample size (n) of 7 squirrels. Since the sample size is less than 30, we use the t-distribution with 7-1=6 degrees of freedom (df).
Firstly, we find the t-score that corresponds to the 95% confidence level for this degrees of freedom, which can be obtained using a t-distribution table or calculator.
Next, we calculate the standard error of the mean (SEM) using the formula SEM = s / √ n. Then we utilize the formula for the confidence interval:
Confidence Interval = μ ± (t-score × SEM).
Once we have the t-score and SEM, we can calculate the upper and lower bounds of the confidence interval. This gives us the range within which the true mean weight of the squirrels is likely to fall, with 95% certainty.