Question

Joan’s nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of planting trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 8 plantings during the past month follow (times in hours):

1.7        2.6       2.2       2.4       2.3       2.6       1.4       2.3

1. Develop a 95% confidence interval for the population mean
2. At a 0.95 degree of confidence, can we conclude that the population mean tree-planting time is 2 hours? Explain.

Answer 1

a. First we will find mean and standard deviation

Create the following table.

data	data-mean	(data - mean)2
1.7	-0.4875	0.23765625
2.6	0.4125	0.17015625
2.2	0.0125	0.00015625
2.4	0.2125	0.04515625
2.3	0.1125	0.01265625
2.6	0.4125	0.17015625
1.4	-0.7875	0.62015625
2.3	0.1125	0.01265625

Find the sum of numbers in the last column to get.

So standard deviation is

t value for 7 df for 95% CI is TINV(0.05,7)=2.365

So Margin of Error is

Hence CI is

b. As 2 lies in the range, so we conclude that the population mean tree-planting time is 2 hours