Question

The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers.

Soil water content from field I: x1; n1 = 72

15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.5 11.1

Soil water content from field II: x2; n2 = 80

12.1 10.2 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.8 14.0 14.2

^{Answer the following questions and show all steps
(don't leave any blank or skip any). All steps and answers are
handwritten.}

1. Compute the sample mean x and sample standard deviation s of soil water content for the field I and for field II.

2. Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 95% confidence interval for μ1 – μ2.

3. Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, is the population mean soil water content of the field I higher than that of the field II

4.Which distribution (Standard Normal or Student’s t) did you use? Explain why? Do you need information about the original soil water content distributions?

5. Use α = 0.01 to test the claim that the population mean soil water content of field I is higher than that of field II. Please provide the following information:

(a) What is the level of significance? State the null and alternative hypotheses.

(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

(e) Interpret your conclusion in the context of the application.

Answer #1

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers.
Soil water content from field I: x1; n1 = 72
15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2
15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0
13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5
13.1 14.7 12.5...

We want to compare the
soil water content (% water by volume) of two fields growing bell
peppers.
The claim is that the two fields have different soil water
content.
Use the data below to test the hypothesis that the fields have
different soil water content.
Field 1 is in list1 and Field 2 is in list2.
We do not know whether the water content values are normally
distributed or not, but their variances are equal.
Provide your answers below....

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers. Soil water content
from field I: x1; n1 = 72 15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1
14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8
9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2
13.8 14.6 10.2 11.5 13.1 14.7 12.5...

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To test for any significant difference in the number of hours
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Machine
1
Machine
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Machine
3
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6.4
8.8
10.9
9.7
7.9
7.6
10.3
12.6
5.5
9.5
9.6
11.8
7.5
10.3
10.2
10.7
8.4
9.3
9.0
11.0
7.5
10.3
8.8
11.4
a) Use Fisher's LSD procedure to test for the equality of the
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Use the data in Bank Dataset to answer this question.
Construct a 95% confidence interval for the mean increase in
deposits. Note that the population standard deviation σ is not
known in this case. Instead the sample standard deviation s should
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