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 plantings of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use 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 (times in hours).
1.7 1.5 2.6 2.2 2.4 2.3 2.6 3 1.4 2.3
With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. b. Compute the sample mean. c. Compute the sample standard deviation. d. What is the p-value?e. What is your conclusion?

We conclude that mean tree-planting time does not differs from two hours.

Step-by-step explanation:

We are given the following in the question:

1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3, 1.4, 2.3

b) Sample mean

c) Sample standard deviation

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 2.4

Population mean, μ = 2 hours

Sample mean, = 2.2 hours

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 0.516 hours

a) First, we design the null and the alternate hypothesis

We use two-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

d) P-value = 0.251453

e) Conclusion:

Since, p value is greater than thee significance level, we fail to reject the null hypothesis and accept it.

Thus, we conclude that mean tree-planting time does not differs from two hours.