12 squirrels were found to have an average weight of 10.5 ounces with a sample standard deviation is 0.25. Find the 95% confidence interval of the true mean weight
95% = mean ± 1.96 SEm
SEm = SD/√n
To find the 95% confidence interval of the true mean weight, we can use the following formula:
Confidence interval = sample mean ± (critical value) × (standard deviation / √sample size).
First, let's find the critical value corresponding to a 95% confidence level. You can look up this value in the standard normal distribution table or use statistical software. For a 95% confidence level, the critical value is approximately 1.96.
Next, plug in the given values into the formula:
Sample mean = 10.5 ounces
Standard deviation = 0.25 ounces
Sample size = 12 squirrels
Critical value = 1.96 (for a 95% confidence level)
Now calculate the confidence interval:
Confidence interval = 10.5 ± (1.96) × (0.25 / √12)
To calculate the square root of 12, you can use a calculator or approximate it as √12 ≈ 3.464.
Confidence interval = 10.5 ± (1.96) × (0.25 / 3.464)
Next, calculate the value inside parentheses:
Value inside parentheses = 0.25 / 3.464 ≈ 0.0721
Now, calculate the upper and lower bounds of the confidence interval:
Upper bound = 10.5 + (1.96) × 0.0721 ≈ 10.5 + 0.1416 ≈ 10.6416
Lower bound = 10.5 - (1.96) × 0.0721 ≈ 10.5 - 0.1416 ≈ 10.3584
So, the 95% confidence interval of the true mean weight is approximately 10.3584 ounces to 10.6416 ounces.