1.16 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.16 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.97 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.77 1.17 1.57 2.62 1.66 2.05 LAUSE SALT The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.484, 1.612, and 0.294, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3% ? Car out a test of the appropriate hypotheses at significance level 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. ⒸH₂: H=3 H₂: H=3 ⒸH₂: H=3 H₂H <3 ⒸH₂: H=3 H₁: H=3 ⒸH₁: H=3 H₂: > 3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = What can you conclude? O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Would your conclusion be different if a = 0.05 had been used? O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%
1.16 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.16 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.97 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.77 1.17 1.57 2.62 1.66 2.05 LAUSE SALT The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.484, 1.612, and 0.294, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3% ? Car out a test of the appropriate hypotheses at significance level 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. ⒸH₂: H=3 H₂: H=3 ⒸH₂: H=3 H₂H <3 ⒸH₂: H=3 H₁: H=3 ⒸH₁: H=3 H₂: > 3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = What can you conclude? O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. Would your conclusion be different if a = 0.05 had been used? O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage of organic matter in this type of soil is something other than 3%
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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![# Investigating Soil Organic Matter Content
**Data Collection**
A random sample of soil specimens was obtained, and the percentage of organic matter in the soil was determined for each specimen as follows:
`1.16, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45`
`0.16, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69`
`3.97, 3.17, 3.03, 2.21, 0.69, 4.57, 3.31, 1.17`
`0.77, 1.17, 1.57, 2.62, 1.66, 2.05`
**Statistical Analysis**
The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are `2.484`, `1.612`, and `0.294`, respectively.
**Key Question**
Does this data suggest that the true average percentage of organic matter in such soil is different from 3%? Conduct a hypothesis test at a significance level of 0.10.
*Note: A normal probability plot of the data shows an acceptable pattern given the reasonably large sample size.*
### Hypotheses
State the appropriate hypotheses:
1. \( H_0: \mu = 3 \)
\( H_a: \mu \neq 3 \)
2. \( H_0: \mu = 3 \)
\( H_a: \mu < 3 \)
3. \( H_0: \mu = 3 \)
\( H_a: \mu > 3 \)
### Calculation
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
- \( t = \) [Input required]
- P-value = [Input required]
### Conclusion
Based on the computed values, decide:
- Reject the null hypothesis: There is enough evidence to conclude that the true average percentage of organic matter in this type of soil is different from 3%.
- Fail to reject the null hypothesis: There is not enough evidence to conclude that the true average percentage of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdd779ee-39b4-455c-9a15-b1302cac6e33%2Ffd83549f-4083-4781-ab21-07c62d507869%2Fz77h7h8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Investigating Soil Organic Matter Content
**Data Collection**
A random sample of soil specimens was obtained, and the percentage of organic matter in the soil was determined for each specimen as follows:
`1.16, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45`
`0.16, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69`
`3.97, 3.17, 3.03, 2.21, 0.69, 4.57, 3.31, 1.17`
`0.77, 1.17, 1.57, 2.62, 1.66, 2.05`
**Statistical Analysis**
The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are `2.484`, `1.612`, and `0.294`, respectively.
**Key Question**
Does this data suggest that the true average percentage of organic matter in such soil is different from 3%? Conduct a hypothesis test at a significance level of 0.10.
*Note: A normal probability plot of the data shows an acceptable pattern given the reasonably large sample size.*
### Hypotheses
State the appropriate hypotheses:
1. \( H_0: \mu = 3 \)
\( H_a: \mu \neq 3 \)
2. \( H_0: \mu = 3 \)
\( H_a: \mu < 3 \)
3. \( H_0: \mu = 3 \)
\( H_a: \mu > 3 \)
### Calculation
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
- \( t = \) [Input required]
- P-value = [Input required]
### Conclusion
Based on the computed values, decide:
- Reject the null hypothesis: There is enough evidence to conclude that the true average percentage of organic matter in this type of soil is different from 3%.
- Fail to reject the null hypothesis: There is not enough evidence to conclude that the true average percentage of
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