Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particuler landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost estimatiing purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual tim from a sample of 10 plantings during the past menth follow (times in hours). 2.9 1.4 22 15 1.6 2.6 23 22 25 2.1 With a 0.05 level of significance, test to see whether the mean tree planting time dfers from twe heurs. a. State the null and alternative hypotheses. Ho Select your answer - Select your anewer 2 b. Compute the sample mean. (to 2 decimals) e. 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- enough evidence to prove that the mean tree-planting time differs from 2 hours. Select your answer reject the null hypothesis. There

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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**Joan's Nursery Analysis**

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 time from a sample of 10 plantings during the past month follow (times in hours):

**Data:**
2.9, 1.6, 1.4, 2.6, 2.3, 2.2, 2.5, 2.2, 1.5, 2.1

**Statistical Analysis:**

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.**

   \( H_0: \mu = 2 \)

   \( H_a: \mu \neq 2 \)

b. **Compute the sample mean.**
   - (Round to 2 decimals)

c. **Compute the sample standard deviation.**
   - (Round to 4 decimals)

d. **Find the test statistic and p-value.** (Use Table 2 in Appendix B.)
   - (Round to 3 decimals)

e. **Conclusion:**
   - Based on the test, reject the null hypothesis if there is significant evidence to prove the mean tree-planting time differs from 2 hours. Otherwise, do not reject the null hypothesis.
Transcribed Image Text:**Joan's Nursery Analysis** 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 time from a sample of 10 plantings during the past month follow (times in hours): **Data:** 2.9, 1.6, 1.4, 2.6, 2.3, 2.2, 2.5, 2.2, 1.5, 2.1 **Statistical Analysis:** 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.** \( H_0: \mu = 2 \) \( H_a: \mu \neq 2 \) b. **Compute the sample mean.** - (Round to 2 decimals) c. **Compute the sample standard deviation.** - (Round to 4 decimals) d. **Find the test statistic and p-value.** (Use Table 2 in Appendix B.) - (Round to 3 decimals) e. **Conclusion:** - Based on the test, reject the null hypothesis if there is significant evidence to prove the mean tree-planting time differs from 2 hours. Otherwise, do not reject the null hypothesis.
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