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

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 93

1131.0 58

273.0 46

254.0 62

111.0 26

154.0 27

30.0 17

What are the null and alternative hypotheses?

Answer #1

65 | 30 |

402 | 43 |

1568 | 93 |

1131 | 58 |

273 | 46 |

254 | 62 |

111 | 26 |

154 | 27 |

30 | 17 |

The Scatterplot using Excel is

The Value of linear correlation coefficient using Excel Command is, "=correl(x,y)"

where x is "Court Income" And y is "Justice Salary"

We get, r=correlation= 0.8703

The Null Hypothesis is

H_{0}: There is no correlation between court incomes and
justice salaries

Versus

H_{a}: There is correlation between court incomes and
justice salaries

So therefore the p value corresponding to r=0.8703 using Pearsons table is 0.024

p-value=0.024

Here, a=level of significance = 0.05 - Given

so therefore, p-value<a

so therefore we fail to accept H_{0}.

Conclusion: There is Sufficient evidence to conclude that there is linear correlation between court incomes and justice salaries.

That is, It Appear that Justice 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 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...

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 64.0 402.0 1568.0 1130.0...

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.
Construct a scatterplot, find the value of the linear correlation
coefficient r, and find the P-value using alphaαequals=0.050.05.
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
66.066.0
403.0403.0
1566.01566.0
1130.01130.0
272.0272.0
253.0253.0...

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...

court income
64.0
404.0
1568.0
1130.0
271.0
250.0
110.0
152.0
34.0
justice salary
31
44
93
57
46
62
26
27
19
Listed are amounts of court income and salaries paid to the town
justices. All amounts are in thousands of dollars.
The percent of variations in Justice Salary that can be
explained by Court Income is, approximately = ______ (answer with a
percent rounded to the hundredths decimal place)

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