In a study of termite populations in Swaziland, the following data were gathered on the percentage of termites that were classified as "major workers" at seven randomly selected sites:37.6 20.0 28.8 29.9 51.9 13.6 34.5 29.0
a)Use the given data to produce a point estimate of , the true mean percentage of termites that are "major workers." (5 pts)
b) Use the given data to produce an unbiased point estimate of , the population variance of the percentage of termites that are "major workers." (5 pts)
Elesha.. I don't understand your answers
To find the point estimate of the true mean percentage of termites that are "major workers," you need to calculate the sample mean. Here's how you can do it:
a) Step-by-step solution:
1. Add up all the given data values: 37.6 + 20.0 + 28.8 + 29.9 + 51.9 + 13.6 + 34.5 + 29.0 = 245.3
2. Divide the sum by the number of data points (7) to calculate the sample mean: 245.3 / 7 ≈ 35.04
3. Therefore, the point estimate of the true mean percentage of termites that are "major workers" is approximately 35.04%.
To find the unbiased point estimate of the population variance, you need to calculate the sample variance using a formula that corrects for bias. Follow these steps:
b) Step-by-step solution:
1. Calculate the sample mean (µ) by following the steps mentioned in part (a), which gives you µ ≈ 35.04.
2. Subtract the sample mean from each data point and square the result: (37.6 - 35.04)², (20.0 - 35.04)², (28.8 - 35.04)², (29.9 - 35.04)², (51.9 - 35.04)², (13.6 - 35.04)², (34.5 - 35.04)², (29.0 - 35.04)².
3. Add up all the squared differences: (37.6 - 35.04)² + (20.0 - 35.04)² + (28.8 - 35.04)² + (29.9 - 35.04)² + (51.9 - 35.04)² + (13.6 - 35.04)² + (34.5 - 35.04)² + (29.0 - 35.04)² = 207.4888.
4. Divide the sum by the number of data points minus 1 (n - 1), where n is the total number of data points (7): 207.4888 / 6 = 34.58147
5. Therefore, the unbiased point estimate of the population variance is approximately 34.58147.
Note: The square root of the unbiased point estimate of the population variance can be taken to find the unbiased point estimate of the population standard deviation.
.45272
.8549