Help please! any help is appreciated

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

MrRissso [65]

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 $\mu$ = true average percentage of organic matter

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 One-sample t-test statistics 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, the test statistics = $\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }$ ~ $t_2_9$

= -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 sufficient evidence to reject our null hypothesis 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 insufficient evidence to reject our null hypothesis 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.

8 0

3 years ago

Find the geometric mean between each pair of numbers.40 and 15

kirill [66]

Given a N quantity of numbers, the Geometric Mean is equal to the N-th root of product of the N numbers

In this case, we have two numbers, then we need to multiply them and take square root:

$\sqrt{40\cdot15}=\sqrt[]{600}=\sqrt[]{100\cdot6}=\sqrt[]{100}\cdot\sqrt[]{6}=10\sqrt[]{6}$

The answer is:

10√6

Rounded is Approximately 24.5

8 0

1 year ago

The high for a winter day in Sitka,

m_a_m_a [10]

Answer:

The maximum temperature will be -10°C, then if T represents the temperature, we can write this as:

T ≤ -10°C

And the minimum temperature will be -25°C, then we must have that:

T ≥ -25°C

if we use both conditions, we will have:

-25°C ≤ T ≤ -10°C

We can write this range:

[-25°C, -10°C]

Where the [] symbols mean that the extremes are possible temperatures.

The length of the range will be:

-10°C - 25°C = 15°C.

3 0

3 years ago

Rachael can paint a room in 9 hours. Kelsey can paint same room in 15 hours. How long if they paint it together.

ElenaW [278]

Answer:

6 hours

Step-by-step explanation:

because if they work together it will be 9 hours slower than Kelsey's time alone.

not sure if correct

7 0

3 years ago

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Audrey has .x pounds of red grapes and y pounds of

mojhsa [17]

We are looking at points in the form (x, y).

Let x = pounds of red grapes

Let y = pounds of green grapes

Audrey has less than 5 pounds of grapes. Here is where I think you made a typo. The question should indicate if Audrey has 5 pounds less of red grapes or green grapes.

Go back and check your original problem and then come back.

6 0

3 years ago

Read 2 more answers