# Statistic

PROBLEM 4

Classified ads in the Ithaca Journal offered several used Toyota Corollas for sale. Listed

below are the ages of the cars and the advertised prices.

Age (yr) Price Advertised ($)

1 13,990

1 13,495

3 12,999

4 9,500

4 10,495

5 8,995

5 9,495

6 6,999

7 6,950

7 7,850

8 6,999

8 5,995

10 4,950

10 4,495

13 2,850

(a) Report the linear correlation coefficient value and comment on the form, the

direction, and strength of association between the age of a car and the advertised

price.

(b) Report the equation of the least-squares regression line. Interpret the coefficients.

(c) Report and interpret the value of the coefficient of determination.

(d) Carry out a T-test about correlation ( H1:p≠0). Use a 5% level of significance.

EXPECTATIONS

Draw graphs and charts when appropriate and necessary to demonstrate your

reasoning! Label all graphs and charts!

Display formulas. Write complete sentences to summarize your conclusions.

If use any table values, clearly state which tables you used (e.g. Table A-2, etc.).

You may attach your excel output when appropriate or necessary (e.g. a scatterplot,

etc.)

HYPOTHESIS TESTING QUESTIONS

Your work for all statistical hypothesis testing questions should include the following:

1. Established Ho and Ha.

2. Summary statistics (either computed or given in the problem)

3. The name of the test (e.g. 2sampleTtest or T-test about correlation, etc.)

4. A formula to compute a test statistic (e.g. 1Prop-Z test statistic, etc.)

5. A p-value of the test and/or a critical value from a statistical table.

6. Clearly state the decision rule you use the reach a conclusion. (You may have to

sketch a graph to show rejection regions.) Do you “Reject Ho” or do you “Fail to

Reject Ho”?

7. State your conclusion in plain language. Use complete sentences.

Answer rating (rated one time)

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xxxxxxxxxx ads in xxx xxxxxx xxxxxxx xxxxxxx xxxxxxx used Toyota xxxxxxxx xxx xxxxx xxxxxx

xxxxx are the xxxx xx the cars and xxx advertised prices.

(a) xxxxxx the linear xxxxxxxxxxx xxxxxxxxxxx value and comment xx xxx form, the

xxxxxxxxxx and strength of xxxxxxxxxxx between the xxx of x xxx and xxx xxxxxxxxxx

xxxxxx

The value xx xx xxxxx using xxxxx xxxxxxxxx The xxxxx xxxx shows xx xxxxxxx xxxxxxxxxxxx xxxxxxx age and price xxxxxxxxxxx xx means xx xxx xxx of car xxxxxxxxxx the price on advertisement decreases.

The form is xxxxxx xxxxxxxxx xxx xxxxxxxxx xx xxxxxxxx and the strength xx xxxxxxxxxxx xx xxxxxx inverse.

(b) xxxxxx the xxxxxxxx xx the least-squares regression xxxxx Interpret the coefficients.

xxxxxxxxxxxxx | Y= xxxxx |

SD xx xxxxxxxx | SDy=5305.990064 |

r=-0.98

*xxxxxxxxx Y* x *x* + *x X*

xxxxx xxx slope *x* xxx intercept *x* xxx calculated in the xxxxxxxxx order:

xxxxxxx x xxxxxxxxxxxx xx xxxxxxx

a= xxxxxxxxxxxx x xxxxxxxxxxx

Y=875.12 xxxxxxxxx

xxxxxxxxx means

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## Answer

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xxxxx**Coefficient xxxxxxx**

x-axis x year

xxxxxx x price**Correlation xxxxxxxxxxx**

xxxxxxxxxxxxx X x xxxx

= -.972

**(b)**

xxxxxxxx xx the xxxxxxxxxxxxx xxxxxxxxxx line

xx xxxx

a=meanY- x xxxxx

b=rxs.dX/S.dY

b= xxxxxx xxxxxxxxxxxxxxxx

xxxxxxxx

a= 14285.9

14285.9-.959.045X

**(c) T-test**

xxxxxxxxxxx of xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx

=.972^2

xxxxxx