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 plantings of 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 10 plantings during the past month follow (times in hours).

1.8

1.4

2.7

2.1

2.4

2.3

2.6

3.0

1.4

2.3

With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.

(a)State the null and alternative hypotheses.

a)H₀: μ ≤ 2

H_a: μ > 2

b)H₀: μ < 2

H_a: μ ≥ 2

c)H₀: μ = 2

H_a: μ ≠ 2

d)H₀: μ ≥ 2

H_a: μ < 2

e)H₀: μ > 2

H_a: μ ≤ 2

(b)Compute the sample mean.

(c)Compute the sample standard deviation. (Round your answer to three decimal places.)

(d)What is the test statistic? (Round your answer to three decimal places.)

test statistic=

What is the p-value? (Round your answer to four decimal places.)

p-value =

(e)What is your conclusion?

Do not reject H₀. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.

Reject H₀. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.    

Do not reject H₀. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.

Reject H₀. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.

Answer 1

Conclusion - Do not reject H₀. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.