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). 1.6 1.4 2.7 2.3 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,Ha: μ ≤ 2 H0: μ ≤ 2, Ha: μ > 2 H0: μ = 2, Ha: μ ≠ 2 H0: μ < 2, Ha: μ ≥ 2 H0: μ ≥ 2, Ha: 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? (A) 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. (B)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. (C) 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. (D)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.

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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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).

1.6

1.4

2.7

2.3

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.

(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?

(A) 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.

(B)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.

(C) 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.

(D)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.

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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