Question

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 costestimating 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). $$\begin{array}{lllllllll}{1.7} & {1.5} & {2.6} & {2.2} & {2.4} & {2.3} & {2.6} & {3.0} & {1.4} & {2.3}\end{array}$$ With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and altemative hypotheses. b. Compute the sample mean. c. Compute the sample standard deviation. d. What is the $p$ -value? e. What is your conclusion?

          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 costestimating 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).
$$\begin{array}{lllllllll}{1.7} & {1.5} & {2.6} & {2.2} & {2.4} & {2.3} & {2.6} & {3.0} & {1.4} & {2.3}\end{array}$$
With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours.
a. State the null and altemative hypotheses.
b. Compute the sample mean.
c. Compute the sample standard deviation.
d. What is the $p$ -value?
e. What is your conclusion?

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Added by Emily M.

Essentials of Modern Business Statistics

David R. Anderson, Dennis J.… 5th Edition

Chapter 9

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Solved by Expert Joshua Argo

08/20/2021

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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 costestimating 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). $$\begin{array}{lllllllll}{1.7} & {1.5} & {2.6} & {2.2} & {2.4} & {2.3} & {2.6} & {3.0} & {1.4} & {2.3}\end{array}$$ With a .05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and altemative hypotheses. b. Compute the sample mean. c. Compute the sample standard deviation. d. What is the $p$ -value? e. What is your conclusion?

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Transcript

00:01 Okay, so in this question, we are doing a significance test at the 0 .05 level, and we're going to kind of break things out.

00:09 So we have a set of data, and we are trying to see does the mean, we have evidence that the true mean tree planning time is different from two hours.

00:23 And we have all of our data there.

00:24 So the first thing we want to do is write out our hypotheses.

00:28 So our null hypothesis, remember null is dull.

00:33 One in which our data matches what we originally thought, which would be two hours.

00:40 So our null is that our true mean is equal to two hours.

00:45 Also, your null, actually both hypotheses are going to be a population parameter there.

00:54 So either p or row, if you're using greek letters, or mu.

00:59 We're not going to put an x bar there.

01:01 And then your null hypothesis is always equal to.

01:05 And then it tells us we're looking for evidence that it is different from two hours.

01:10 So that is simply just not equal to two hours.

01:15 Sometimes it's also important to specify what your parameter is.

01:19 And in this case, it is the true mean tree planting time, as described in the question.

01:28 All right, so part b, we are going to compute the sample mean.

01:32 I did that in my calculator by running the t test.

01:37 So i did a t test with my data in the calculator, and it gives me my x bar, which is 2 .2...

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