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 one and half 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).

1.5 0.9 2.6 1.6 2.4 3.3 2.6 2.0 2.1 3.1

With a 0.02 level of significance, test to see whether the mean tree-planting time differs from one and half hours.

a. State the null and alternative hypotheses.

Ho: u __ 1.5

Ha: u __ 1.5

b. Compute the sample mean. (to 1 decimal)

c. Compute the sample standard deviation. (to 3 decimals)

d. What is the p-value?

t-value: (to 3 decimals)

p-value:

e. What is your conclusion? We (DO/DO NOT) reject the null. There (IS/IS NOT) enough evidence to prove that the mean tree-planting time differs from 1.5 hours.

Answer 1

x: Sample actual times

a. Hypothesized mean : = 1.5 hours

Null hypothesis and alternate hypothesis

H_o :

H_a :

x: Sample actual times

b. Sample mean

n : sample size =10

Sample mean = 2.2

c.

Sample standard deviation : s

Sample standard deviation : s = 0.743

d.

t-value = 3.0213

For two tailed test :

Degrees of freedom = n-1 = 10-1=9

for 9 degrees of freedom :

p-value = 0.0144

c. t-value = 3.0213

d. p-value = 0.0144

e.

As P-Value i.e. is less than Level of significance i.e (P-value:0.0144 < 0.02:Level of significance); Reject Null Hypothesis
We DO reject the null

There IS enough evidence to prove that the mean tree-planting time differs from 1.5 hours