Compute the sample mean and the sample standard deviation. **Chapter 9: Statistical Inference**Joan's Nursery specializes in custom-designed landscaping for residential areas. 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):- 1.3, 2.8, 2.3, 2.1, 1.5, 1.6, 2.3, 2.7, 2.5, 3.3With 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.**- $H_0: \mu \, \boxed{\leq, =, \ge, <, \neq} \, 2$- $H_a: \mu \, \boxed{\leq, =, \ge, <, \neq} \, 2$**b. Compute the sample mean.**- [Enter value] (to 2 decimals)**c. Compute the sample standard deviation.**- [Enter value] (to 4 decimals)**d. Find the test statistic and p-value.** (Use Table 2 in Appendix B.)- $t \, \boxed{____}$ (to 3 decimals)- $p \text{-value} \, \boxed{\text{Select your answer}}$ **e. What is your conclusion?**- We $\boxed{\text{Select your answer}}$ reject the null hypothesis. There is $\boxed{\text{Select your answer}}$ enough evidence to prove that the mean tree-planting time differs from 2 hours. This exercise guides students through hypothesis testing steps, focusing on real-life data application in a nursery setting.

Given: Data: 1.3, 2.8, 2.3, 2.1, 1.5, 1.6, 2.3, 2.7, 2.5, 3.3 N=10 (a) Hypothesis: For cost…

Answered: Compute the sample mean and the sample…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Compute the sample mean and the sample standard deviation.

**Chapter 9: Statistical Inference**

Joan's Nursery specializes in custom-designed landscaping for residential areas. 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):

- 1.3, 2.8, 2.3, 2.1, 1.5, 1.6, 2.3, 2.7, 2.5, 3.3

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.**

- $H_0: \mu \, \boxed{\leq, =, \ge, <, \neq} \, 2$
- $H_a: \mu \, \boxed{\leq, =, \ge, <, \neq} \, 2$

**b. Compute the sample mean.**

- [Enter value] (to 2 decimals)

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

- [Enter value] (to 4 decimals)

**d. Find the test statistic and p-value.** (Use Table 2 in Appendix B.)

- $t \, \boxed{____}$ (to 3 decimals)
- $p \text{-value} \, \boxed{\text{Select your answer}}$

**e. What is your conclusion?**

- We $\boxed{\text{Select your answer}}$ reject the null hypothesis. There is $\boxed{\text{Select your answer}}$ enough evidence to prove that the mean tree-planting time differs from 2 hours.

This exercise guides students through hypothesis testing steps, focusing on real-life data application in a nursery setting.

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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