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.SpecimenDirectStratified12382343930846059520546636374028888914810941001130126859137968142354 SpecimenDirectStratified153428160017393918191419949420314214048222323230024814251440261914274079 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 =

The random variable is number of seeds detected. There are two dependent samples which are direct…

Answered: Several methods of estimating the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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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	23	8
2	34	39
3	0	8
4	60	59
5	20	54
6	63	63
7	40	28
8	8	8
9	14	8
10	94	100
11	3	0
12	68	59
13	79	68
14	23	54

Specimen	Direct	Stratified
15	34	28
16	0	0
17	39	39
18	19	14
19	94	94
20	3	14
21	40	48
22	23	23
23	0	0
24	8	14
25	14	40
26	19	14
27	40	79

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 =

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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Specimen	Direct	Stratified
1	23	8
2	34	39
3	0	8
4	60	59
5	20	54
6	63	63
7	40	28
8	8	8
9	14	8
10	94	100
11	3	0
12	68	59
13	79	68
14	23	54

Specimen	Direct	Stratified
15	34	28
16	0	0
17	39	39
18	19	14
19	94	94
20	3	14
21	40	48
22	23	23
23	0	0
24	8	14
25	14	40
26	19	14
27	40	79

Specimen	Direct	Stratified
1	23	8
2	34	39
3	0	8
4	60	59
5	20	54
6	63	63
7	40	28
8	8	8
9	14	8
10	94	100
11	3	0
12	68	59
13	79	68
14	23	54

Specimen	Direct	Stratified
15	34	28
16	0	0
17	39	39
18	19	14
19	94	94
20	3	14
21	40	48
22	23	23
23	0	0
24	8	14
25	14	40
26	19	14
27	40	79

Specimen	Direct	Stratified
1	23	8
2	34	39
3	0	8
4	60	59
5	20	54
6	63	63
7	40	28
8	8	8
9	14	8
10	94	100
11	3	0
12	68	59
13	79	68
14	23	54

Specimen	Direct	Stratified
15	34	28
16	0	0
17	39	39
18	19	14
19	94	94
20	3	14
21	40	48
22	23	23
23	0	0
24	8	14
25	14	40
26	19	14
27	40	79