Question

Listed below are amounts of court income and salaries paid to the town justices. 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 alphaα=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 | 406.0 | 1567.0 | 1132.0 | 272.0 | 253.0 | 111.0 | 156.0 | 33.0 |

Justice Salary |
30 | 42 | 91 | 57 | 47 | 62 | 26 | 27 | 17 |

1) What are the null and alternative hypotheses?

A) H_{0}: p=0 , H_{1}: p < 0

B) H_{0}: p=0 , H_{1}: p > 0

C) H_{0}: p=0 , H_{1}: p =/ 0

D) H_{0}: p=/ 0 , H_{1}: p=0

2) Construct a scatterplot.

3) The linear correlation coefficient r is

4) The test statistic t is

5) The P-value is

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

A) It does appear that justices my profit by issuing smaller fines.

B) it does appear that justices is my profit by levying larger fines.

C) it appears that justices profit the same despite the amount of the fines.

D) it does not appear that justices might profit by levying larger fines.

Answer #1

X :- Court Income

Y :- Justice Salary

ΣX = 3995

ΣY = 399

ΣX * Y = 262252

ΣX2 = 4081713

ΣY2 = 21941

Part 1)

To Test :-

H0 :- ρ = 0

H1 :- ρ ≠ 0

Part 2)

part 3)

r = 0.859

Part 4)

Test Statistic :-

t = (r * √(n - 2) / (√(1 - r2))

t = ( 0.8594 * √(9 - 2) ) / (√(1 - 0.7386) )

t = 4.4473

Part 5)

P - value = P ( t > 4.4473 ) = 0.003

Reject null hypothesis if P value < α = 0.05 level of
significance

P - value = 0.003 < 0.05 ,hence we reject null hypothesis

**Conclusion :- There is statistical correlation between
variables**

B) it does appear that justices is might profit by levying larger fines.

Listed below are amounts of court income and salaries paid to
the town justices. 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
alpha
equals0.05
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 Justice_Salary
65.0 30
402.0 43
1568.0 ...

Listed below are amounts of court income and salaries paid to
the town justices. 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 alpha equals0.05 . 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 64.0 405.0 1567.0 1132.0...

Listed below are amounts of court income and salaries paid to
the town justices. all amounts are in thousands of dollars.
Court income 66.0 403.0 1566.0 113.0 270.0 253.0 110.0 156.0
34.0
justice salary 29 46 90 57 44 62 26 27 17
the percent of variations in justice salary that can be
explained by court income is, approximately = _ (answer with a
percent rounded to the hundreths decimal place)

Listed below are amounts of court income and salaries paid to
the town justices for a certain town. All amounts are in thousands
of dollars. Find the (a) explained variation, (b) unexplained
variation, and (c) indicated prediction interval. There is
sufficient evidence to support a claim of a linear correlation, so
it is reasonable to use the regression equation when making
predictions. For the prediction interval, use a 99% confidence
level with a court income of $800,000.
Court_Income Justice_Salary
62...

The data below shows the high temperatures and the times (in
minutes) runners who won a marathon. Construct a scatterplot, find
the value of the linear correlation coefficient r, and find the
P-value using alphaα=0.05. Is there sufficient evidence to conclude
that there is a linear correlation between temperature and winning
times?
Temperature (x)
59
65
47
64
71
74
55
56
Time (y)
146.078
146.739
144.938
144.069
145.307
146.855
148.056
147.564
1) What are the null and alternative hypotheses?...

Listed below are amounts of bills for dinner and the amounts of
the tips that were left. Construct a scatterplot, find the value
of the linear correlation coefficient r, and find the P-value of
r. Determine whether there is sufficient evidence to support a
claim of linear correlation between the two variables. Use a
significance level of α = 0.01. If everyone were to tip with the
same percentage, what should be the value of r?
Bill (dollars) 31.62...

Listed below are annual data for various years. The data are
weights (metric tons) of imported lemons and car crash fatality
rates per 100,000 population. 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 lemon imports and crash
fatality rates? Do the results suggest that imported lemons cause
car fatalities?
Lemon Imports
228
266
357
483
534
Crash...

Listed below are paired data consisting of amounts spent on
advertising (in millions of dollars) and the profits (in millions
of dollars). Determine if there is a significant negative linear
correlation between advertising cost and profit . Use a
significance level of 0.01 and round all values to 4 decimal
places.
Advertising Cost
Profit
3
14
4
14
5
25
6
22
7
27
8
18
9
33
10
26
11
36
12
22
Ho: ρ = 0
Ha: ρ...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 5 minutes ago

asked 6 minutes ago

asked 7 minutes ago

asked 7 minutes ago

asked 11 minutes ago

asked 15 minutes ago

asked 20 minutes ago

asked 20 minutes ago

asked 23 minutes ago

asked 23 minutes ago