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Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Constr

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

Hello!

Full text:

Listed below are amounts of court income and salaries paid to the town justice. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P value using α = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines?

Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0

Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18

a. What are the null and alternative hypotheses?

To test if there is a linear correlation between the court income and the justice salary, you have to use the following hypotheses:

H₀: ρ = 0

H₁: ρ ≠ 0

b. Construct a scatterplot. See attachment.

c. The linear correlation coefficient r is: _____.

$r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]} }$

n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123

r= 0.86

d. The P value is: _____.

This test is two-tailed and so is its p-value. I've calculated it using a statistics software:

p-value: 0.0027

e. Based on the results, does it appear that justices might profit by levying larger fines?

Using the p-value approach, the decision rule is:

If the p-value ≤ α, reject the null hypothesis.

If the p-value > α, do not reject the null hypothesis.

The calculated p-value is less than the significance level, then the decision is to reject the null hypothesis.

At a 5% significance level you can conclude that there is a linear correlation between the "court income" and the "Justice salary"

I hope this helps!

6 0

3 years ago

The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?

Aleksandr [31]

Answer:

The new pyramid has a volume that is half the volume of the original pyramid.

Step-by-step explanation:

The volume of a pyramid is given by the following equation:

$V = \frac{h*l*w}{3}$

In which h is the height, l is the length and w is the width.

Modified volume:

height doubled, length and width cut in half. So

$h = 2h, l = 0.5l, w = 0.5w$

$V_{M} = \frac{2h*0.5l*0.5l}{3} = \frac{0.5*h*l*w}{3} = 0.5\frac{h*l*w}{3}$ = 0.5V[/tex]

That is

The new pyramid has a volume that is half the volume of the original pyramid.

6 0

3 years ago

The table shows a proportional relationship between x

lakkis [162]

What’s the question it’s not showing up for me or you just didn’t type it

7 0

3 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

A recent survey found that 3 out of every 7 people like birds. If 3500 people were surveyed, how many like birds?

photoshop1234 [79]

1500 hopefully that helps

8 0

3 years ago