Question

An ecologist randomly samples 14plants of a specific species and measures their heights. He finds that this sample has a mean of 17 cm and a standard deviation of 1 cm. If we assume that the height measurements are normally distributed, find a 99% confidence interval for the mean height of all plants of this species. Then find the lower limit and upper limit of the 99% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
Lower limit
Upper Limit

Answer 1

To find a 99% confidence interval for the mean height of all plants of a specific species, use the formula CI = (sample_mean - z * (std_dev/sqrt(n)), sample_mean + z * (std_dev/sqrt(n))). Substituting the given values, the lower limit is 16.842 cm and the upper limit is 17.158 cm.

Step-by-step explanation:

To find a 99% confidence interval for the mean height of all plants of the specific species, we can use the formula:

CI = (sample_mean - z * (std_dev/sqrt(n)), sample_mean + z * (std_dev/sqrt(n)))

Here, the sample mean is 17 cm, the standard deviation is 1 cm, and the sample size is 14. The critical value, z, for a 99% confidence interval is approximately 2.576.

Substituting these values into the formula, we get:
CI = (17 - 2.576 * (1/sqrt(14)), 17 + 2.576 * (1/sqrt(14)))

Calculating the lower and upper limits of the confidence interval, we find:
Lower limit = 16.842
Upper limit = 17.158