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 costestimating 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 1.5 2.6 2.2 2.4 2.3 2.6 3.0 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 is two hours.

Step-by-step explanation:

We are given the following data about plantings in hours 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) Formula for 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) the null and the alternate hypothesis are

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

Formula:

Putting all the values, we have

d) We calculate the p-value from the table.

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.

The mean tree-planting time is two hours.

Given that ,

Actual times from a sample of 10 plantings during the past month n = 10

The observation are = 1.7,  1.5, 2.6,  2.2,  2.4,  2.3, 2.6,  3.0,  1.4, 2.3.

Sum of all the observations = 1.7+1.5+2.6+ 2.2+ 2.4 +2.3 +2.6 +3.0 +1.4 +2.3 =  22.

                           Mean = = 2.2

The sample mean is  2.2 .

Where are data points and x is the mean and the n is the no. of samples

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.

Using two tailed test to perform this hypothesis  

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

For more information about probability click the link given below.

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many reason,

step-by-step explanation: