Several methods of estimating the number of seeds in soil samples have been developed by ecologists. An article gave the accompanying data on the number of seeds detected by the direct method and by the stratified method for 27 soil specimens. Specimen Direct Stratified 1 21 6 2 32 38 3 0 6 4 60 58 5 20 52 6 61 61 7 40 26 8 6 6 9 12 6 10 92 100 11 1 0 12 66 58 13 78 66 14 21 52 Specimen Direct Stratified 15 32 26 16 0 0 17 38 38 18 18 12 19 92 92 20 1 12 21 40 46 22 21 21 23 0 0 24 6 12 25 12 40 26 18 12 27 40 78 Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using ? = 0.05. (Use ?direct − ?stratified.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Fail to reject H0. We do not have convincing evidence that the mean number of seeds detected differs for the two methods.Reject H0. We have convincing evidence that the mean number of seeds detected differs for the two methods. Fail to reject H0. We have convincing evidence that the mean number of seeds detected differs for the two methods.Reject H0. We do not have convincing evidence that the mean number of seeds detected differs for the two methods.

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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Question

Several methods of estimating the number of seeds in soil samples have been developed by ecologists. An article gave the accompanying data on the number of seeds detected by the direct method and by the stratified method for 27 soil specimens.

Specimen	Direct	Stratified
1	21	6
2	32	38
3	0	6
4	60	58
5	20	52
6	61	61
7	40	26
8	6	6
9	12	6
10	92	100
11	1	0
12	66	58
13	78	66
14	21	52

Specimen	Direct	Stratified
15	32	26
16	0	0
17	38	38
18	18	12
19	92	92
20	1	12
21	40	46
22	21	21
23	0	0
24	6	12
25	12	40
26	18	12
27	40	78

Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using

? = 0.05.

(Use ?_direct − ?_stratified.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df. (Round your answer down to the nearest whole number.)

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

Fail to reject H₀. We do not have convincing evidence that the mean number of seeds detected differs for the two methods.Reject H₀. We have convincing evidence that the mean number of seeds detected differs for the two methods. Fail to reject H₀. We have convincing evidence that the mean number of seeds detected differs for the two methods.Reject H₀. We do not have convincing evidence that the mean number of seeds detected differs for the two methods.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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