With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.State the null and alternative hypotheses. **Hypothesis Testing for Mean Tree-Planting Time****Context:**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 typically use two hours of labor time for the planting of a medium-sized tree. The actual planting times from a sample of 10 plantings during the past month are recorded as follows (in hours): 1.4, 1.5, 1.3, 2.2, 2.1, 2.7, 2.6, 2.3, 2.3, 3.2.**Objective:**With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.**Steps:**a. **State the null and alternative hypotheses:**- $ H_0: \mu = 2 $ (The mean planting time is 2 hours)- $ H_a: \mu \neq 2 $ (The mean planting time differs from 2 hours)b. **Compute the sample mean.**Fill in the box with the calculated sample mean (rounded to 2 decimals).c. **Compute the sample standard deviation.**Fill in the box with the calculated sample standard deviation (rounded to 4 decimals).d. **Find the test statistic and $ p $-value.**Use Table 2 in Appendix B to find the $ t $-value and corresponding $ p $-value, and fill in the boxes (with $ t $ rounded to 3 decimals).e. **Conclusion:**State whether you reject or fail to reject the null hypothesis. Also, indicate if there is enough evidence to prove that the mean tree-planting time differs from 2 hours.This exercise involves statistical analysis to verify whether real-world data differs significantly from expected values, specifically in the context of labor time for tree plantings at a nursery.

Given that, Sample size n=10 a. Hypothesis: H0:μ=2 (That is, the population mean tree planting time…

Answered: 2.2 2.1 2.2 2.6 2.3 3.2 With a 0.05…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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

State the null and alternative hypotheses.

**Hypothesis Testing for Mean Tree-Planting Time**

**Context:**
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 typically use two hours of labor time for the planting of a medium-sized tree. The actual planting times from a sample of 10 plantings during the past month are recorded as follows (in hours): 1.4, 1.5, 1.3, 2.2, 2.1, 2.7, 2.6, 2.3, 2.3, 3.2.

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

**Steps:**

a. **State the null and alternative hypotheses:**

- $ H_0: \mu = 2 $ (The mean planting time is 2 hours)
- $ H_a: \mu \neq 2 $ (The mean planting time differs from 2 hours)

b. **Compute the sample mean.**

Fill in the box with the calculated sample mean (rounded to 2 decimals).

c. **Compute the sample standard deviation.**

Fill in the box with the calculated sample standard deviation (rounded to 4 decimals).

d. **Find the test statistic and $ p $-value.**

Use Table 2 in Appendix B to find the $ t $-value and corresponding $ p $-value, and fill in the boxes (with $ t $ rounded to 3 decimals).

e. **Conclusion:**

State whether you reject or fail to reject the null hypothesis. Also, indicate if there is enough evidence to prove that the mean tree-planting time differs from 2 hours.

This exercise involves statistical analysis to verify whether real-world data differs significantly from expected values, specifically in the context of labor time for tree plantings at a nursery.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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