A sociologist is interested in the relation betweenx= number of job changes andy= annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information.

x(number of job changes)	4	5	3	6	1	5	9	10	10	3
y(Salary in $1000)	32	34	35	32	32	38	43	37	40	33

In this setting we havex=56,y=356,x²=402,y²=12,804, andxy=2073.(a) Findx,y,b, and the equation of the least-squares line. (Round your answers forxandyto two decimal places. Round your least-squares estimates to four decimal places.)

x	=
y	=
b	=
	=	+ x

(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x,y).

(c) Find the sample correlation coefficientrand the coefficient of determination. (Round your answers to three decimal places.)

r=
r2=

What percentage of variation inyis explained by the least-squares model? (Round your answer to one decimal place.) % (d) Test the claim that the population correlation coefficientis positive at the 5% level of significance. (Round your test statistic to three decimal places.)

t=

Find or estimate theP-value of the test statistic. P-value > 0.250

0.125 <P-value < 0.250

0.100 <P-value < 0.125

0.075 <P-value < 0.100

0.050 <P-value < 0.075

0.025 <P-value < 0.050

0.010 <P-value < 0.025

0.005 <P-value < 0.010

0.0005 <P-value < 0.005

P-value < 0.0005 Conclusion

Reject the null hypothesis. There is sufficient evidence that> 0.

Reject the null hypothesis. There is insufficient evidence that> 0.

Fail to reject the null hypothesis. There is sufficient evidence that> 0.

Fail to reject the null hypothesis. There is insufficient evidence that> 0.

(e) If someone hadx=6job changes, what does the least-squares line predict fory, the annual salary? (Round your answer to two decimal places.) thousand dollars______ (f) FindS_e. (Round your answer to three decimal places.) S_e= (g) Find a 90% confidence interval for the annual salary of an individual withx=6job changes. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

(h) Test the claim that the slopeof the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.)

t=

Find or estimate theP-value of the test statistic. P-value > 0.250

0.125 <P-value < 0.250

0.100 <P-value < 0.125

0.075 <P-value < 0.100

0.050 <P-value < 0.075

0.025 <P-value < 0.050

0.010 <P-value < 0.025

0.005 <P-value < 0.010

0.0005 <P-value < 0.005

P-value < 0.0005 Conclusion

Reject the null hypothesis. There is sufficient evidence that> 0.

Reject the null hypothesis. There is insufficient evidence that> 0.

Fail to reject the null hypothesis. There is sufficient evidence that> 0.

Fail to reject the null hypothesis. There is insufficient evidence that> 0. (i) Find a 90% confidence interval forand interpret its meaning. (Round your answers to three decimal places.)

lower limit
upper limit

Interpretation

For each additional job change, the annual salary increases by an amount that falls outside the confidence interval.

For each additional job change, the annual salary increases by an amount that falls within the confidence interval.

For each less job change, the annual salary increases by an amount that falls outside the confidence interval.

For each less job change, the annual salary increases by an amount that falls within the confidence interval.