Question

Alba 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 of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use at most two hours of labor time for the planting of a medium-sized tree.

Actual times from a sample of 10 plantings during the past month follow (time in hours): 1.7 1.5 2.6. 2.2   2.4 2.3 2.6 3. 1.4. 2.3

Is there sufficient evidence that the mean tree planting time is more than two hours for planting a medium-sized tree? What is your conclusion?

Please provide the answer for Ho, H1, P-value, and conclusion.

Please make sure to provide clear easy understandable answers and explain the conclusion in writing. Thank you in Advance

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2
Alternative Hypothesis, Ha: μ > 2

Rejection Region
This is right tailed test, for α = 0.05 and df = 9
Critical value of t is 1.833.
Hence reject H0 if t > 1.833

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.2 - 2)/(0.5164/sqrt(10))
t = 1.225

P-value Approach
P-value = 0.1258
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the mean tree planting time is more than two hours for planting a medium-sized tree