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swat32
3 years ago
11

A pitcher of fruit punch holds 2 gallons. If 9 people share the entire pitcher equally, how much punch does each person get in a

fraction?
Mathematics
1 answer:
EastWind [94]3 years ago
8 0
2/9 of a gallon per person.
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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 = <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.

8 0
3 years ago
X+4x +6x= Simplify each expression
lozanna [386]
You add like terms together
1x+4x+6x are like terms

=11x
3 0
2 years ago
Read 2 more answers
3/4(8x-4)=7x+2, I need to find out the answer
laiz [17]

Answer: x = -5

Step-by-step explanation:

First convert 3/4 to decimal= 0.75

0.75 (8x - 4) = 7x + 2

6x - 3 = 7x + 2

Transpose 7x from right hand side to the left hand side

6x - 7x = 2 + 3

-x = 5

x = -5

I hope this helps.

8 0
2 years ago
CAN SOMONE ANSWER THIS
laiz [17]

Your answer is 8,000 minus 6 & 4

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
which transformations of the graph of f(x) = -4^x result in the graph of f(x) = 4^x 3? reflection over the x-axis and shifted 3
Semenov [28]
Reflection over the y-axis and shifted 3 units up
4 0
2 years ago
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