The following data represent soil water content (percent 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

15.1 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 11.3

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

12.1 10.3 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 8.6 14.0 14.1

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to four decimal places.)

x₁ =

s₁ =

x₂ =

s₂ =

(b) 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. (Round your answers to two decimal places.)

lower limit

upper limit

(c) Explain what the confidence interval 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 first field higher than that of the second field?
Because the interval contains only positive numbers, we can say that the mean soil water content of the first field is higher.

Because the interval contains both positive and negative numbers, we cannot say that the mean soil water content of the first field is higher.

Because the interval contains only negative numbers, we can say that the mean soil water content of the second field is higher.

(d) Which distribution did you use? Why?
The standard normal distribution was used because σ₁ and σ₂ are unknown.

The standard normal distribution was used because σ₁ and σ₂ are known.

The Student's t-distribution was used because σ₁ and σ₂ are known.

The Student's t-distribution was used because σ₁ and σ₂ are unknown.

Do you need information about the soil water content distributions?

Both samples are large, so information about the distributions is not needed.

Both samples are small, so information about the distributions is not needed.

Both samples are small, so information about the distributions is needed.

Both samples are large, so information about the distributions is needed.

Question

The following data represent soil water content (percent 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

15.1	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	11.3

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

12.1	10.3	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	8.6	14.0	14.1

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to four decimal places.)

x₁ =
s₁ =
x₂ =
s₂ =

(b) 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. (Round your answers to two decimal places.)

lower limit
upper limit

(c) Explain what the confidence interval 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 first field higher than that of the second field?

Because the interval contains only positive numbers, we can say that the mean soil water content of the first field is higher.

Because the interval contains both positive and negative numbers, we cannot say that the mean soil water content of the first field is higher.

Because the interval contains only negative numbers, we can say that the mean soil water content of the second field is higher.

(d) Which distribution did you use? Why?

The standard normal distribution was used because σ₁ and σ₂ are unknown.

The standard normal distribution was used because σ₁ and σ₂ are known.

The Student's t-distribution was used because σ₁ and σ₂ are known.

The Student's t-distribution was used because σ₁ and σ₂ are unknown.

Do you need information about the soil water content distributions?

Both samples are large, so information about the distributions is not needed.

Both samples are small, so information about the distributions is not needed.

Both samples are small, so information about the distributions is needed.

Both samples are large, so information about the distributions is needed.

Accepted Answer

The given information is the soil water content for the two independent random samples of soil taken…