Final answer:
The lower bound for the 95% confidence interval, given a sample mean of 32, a population standard deviation of 10, and a sample size of 25, is calculated to be 28.08.
Step-by-step explanation:
To calculate the lower bound for the 95% confidence interval given a sample mean of 32, a population standard deviation of 10, and a sample size of 25, we use the formula for a confidence interval:
Confidence Interval (CI) = sample mean ± (z* × (population standard deviation / √ sample size)), where z* is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is typically 1.96 (which can be found in z-score tables or by using statistical software).
Now, we'll calculate the error bound for the mean (EBM) using the population standard deviation of 10, the sample size of 25, and the z-score of 1.96:
EBM = z* × (population standard deviation / √ sample size) = 1.96 × (10 / √25) = 1.96 × (10 / 5) = 1.96 × 2 = 3.92.
Finally, we can find the lower bound of the CI by subtracting the EBM from the sample mean:
Lower Bound = sample mean - EBM = 32 - 3.92 = 28.08.
Therefore, the lower bound for the 95% confidence interval is 28.08.