1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mezya [45]
3 years ago
10

A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specime

n, resulting in the accompanying data (from "Engineering Properties of Soil," Soil Science, 1998: 93–102).1.10 5.09 0.97 1.59 4.60 0.32 0.55 1.450.14 4.47 1.20 3.50 5.02 4.67 5.22 2.693.98 3.17 3.03 2.21 0.69 4.47 3.31 1.170.76 1.17 1.57 2.62 1.66 2.05The values of the sample mean, sample standard deviation,and (estimated) standard error of the mean are2.481, 1.616, and .295, respectively. Does this data suggestthat the true average percentage of organic matterin such soil is something other than 3%? Carry out atest of the appropriate hypotheses at significance level.10. Would your conclusion be different if a 5 .05 hadbeen used? [Note: A normal probability plot of the datashows an acceptable pattern in light of the reasonablylarge sample size.]
Mathematics
1 answer:
MrRissso [65]3 years ago
8 0

Answer:

We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

Step-by-step explanation:

We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;

1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.

Let \mu = <u><em>true average percentage of organic matter</em></u>

So, Null Hypothesis, H_0 : \mu = 3%      {means that the true average percentage of organic matter in such soil is 3%}

Alternate Hypothesis, H_A : \mu \neq 3%      {means that the true average percentage of organic matter in such soil is something other than 3%}

The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                         T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean percentage of organic matter = 2.481%

             s = sample standard deviation = 1.616%

            n = sample of soil specimens = 30

So, <u><em>the test statistics</em></u> =  \frac{2.481-3}{\frac{1.616}{\sqrt{30} } }  ~ t_2_9

                                     =  -1.76

The value of t-test statistics is -1.76.

(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.

(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have <u><em>insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.

You might be interested in
Ans with steps.. Tysm Plzz asap!!
WARRIOR [948]

Answer:

10x^2 + 8x

Step-by-step explanation:

Area of the outer rectangle = 5x(3x + 2) = 15x^2 + 10x

Area of the inner rectangle = x(5x - 2) = 5x^2 - 2x

Area of the shaded region = (15x^2 + 10x) - (5x^2 - 2x)

= 10x^2 + 8x

5 0
3 years ago
Read 2 more answers
I will name you Brainliest. Plz Help Asap 14 points
snow_tiger [21]

Answer: 5

Step-by-step explanation:

2w + 2L = perimeter

2w + 2(4) = 18

2w + 8 = 18

2w = 10

w = 5

7 0
3 years ago
Read 2 more answers
Find the value of this expression if x = 3.<br> x2 + 3/X
Elden [556K]

Answer:

7

Step-by-step explanation:

3 0
2 years ago
83333333333/10000000000 simplified answer
makkiz [27]
8.33333333. You know you can use a calculator.
6 0
3 years ago
Please answer this question correctly :)
Vlada [557]
The answer for this problem is 70
3 0
3 years ago
Other questions:
  • Consider five circles with a radii of 1, 2, 4, 8, and 16 inches. Write your answer in terms of pi r square. Compare the areas an
    11·1 answer
  • Ben originally filled out 6 more applications than henry. Then each boy filled out 4 additional applications, bringing the total
    8·1 answer
  • Solve z2 – 2z – 35 = 0 using the zero product property.
    11·1 answer
  • How can you an area of triangles and trapezoids
    15·1 answer
  • 3/4 Divided by 3/4 equals what
    12·2 answers
  • The ratio of the number of students at the zoo in the morning to the number of students at the zoo in the afternoon was 5:3. The
    9·2 answers
  • The tagnet of the standard angles 0°, 30°,45°,60°and 90°​
    12·1 answer
  • Find the number of choices that are possible if you choose one of 3 kinds of fruit and one of 3 kinds of vegetables.
    7·1 answer
  • What number decreased by 23% is equals 123?
    12·1 answer
  • Find the coordinates of the midpoint of the segment whose endpoints are given W (-3,-7) and X (-8,4)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!