Part C. Compute the sample mean and sample deviation.
Transcribed Image Text: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).
1.4
1.5
1.3
2.2
2.1
2.2
2.7
2.6
2.3
3.2
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.
Ho :
Select your answer - ♥
d: ®H
b. Compute the sample mean.
Select your answer - ▼
a
(to 2 decimals)
C. Compute the sample standard deviation.
(to 4 decimals)
d. Find the test statistic and p-value. (Use Table 2 in Appendix B.)
(to 3 decimals)
p-value
Select your answer -
e. What is your conclusion?
We
- Select your answer
- v reject the null hypothesis. There
Select your answer-
v enough evidence to prove that the mean tree-
planting time differs from 2 hours.
2]
2)
t,
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 + ...
Expert Solution
Step 1
The table that depicts the calculation is shown below:
The mean can be calculated as:
The variance can be calculated as:
The standard deviation can be calculated as:
The test statistic can be calculated as:
The p-value for 9(10-1) degrees of freedom and two taled test is 0.4568, which can be obtained by using the t-distribution table. As the 0.4568>0.05, the null hypothesis is not rejected.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
![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).
1.4
1.5
1.3
2.2
2.1
2.2
2.7
2.6
2.3
3.2
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.
Ho :
Select your answer - ♥
d: ®H
b. Compute the sample mean.
Select your answer - ▼
a
(to 2 decimals)
C. Compute the sample standard deviation.
(to 4 decimals)
d. Find the test statistic and p-value. (Use Table 2 in Appendix B.)
(to 3 decimals)
p-value
Select your answer -
e. What is your conclusion?
We
- Select your answer
- v reject the null hypothesis. There
Select your answer-
v enough evidence to prove that the mean tree-
planting time differs from 2 hours.
2]
2)
t,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3458b95-5123-4489-b2c3-cf4b0d696559%2Fd2e1859b-667b-443d-8c5a-37dff631af60%2F18g9d1g_processed.jpeg&w=3840&q=75)
