Question

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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).

1.7

1.4

2.7

2.2

2.5

2.3

2.6

3.0

1.3

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.

H₀: μ < 2

H_a: μ ≥ 2

H₀: μ ≤ 2

H_a: μ > 2

    

H₀: μ = 2

H_a: μ ≠ 2

H₀: μ > 2

H_a: μ ≤ 2

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.)

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

p-value =

(e)

What is your 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.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.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.

Answer 1

a)

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

b)

sample mena = 2.2

c)

std.deviation = 0.564

d)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.2 - 2)/(0.564/sqrt(10))
t = 1.121

P-value Approach
P-value = 0.2913
As P-value >= 0.05, fail to reject null hypothesis.

e)

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.