Question

A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed.Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?

Answer 1

One sample t-test for population mean would be the most appropriate method.

Explanation:

Following is the data which botanist collected and can use:

• Sample mean
• Sample Standard Deviation
• Sample size (Which is 10)
• Distribution is normal

We have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:

• One-sample z test for population mean
• One-sample t test for population mean

One sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.

Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.

Therefore, One-sample t-test for population mean would be the most appropriate method.