Question

A sociologist is interested in the relation between x = number of job changes and y = 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	3	6	6	1	5	9	10	10	3
y (Salary in $1000)	35	37	36	32	32	38	43	37	40	33

In this setting we have Σx = 57, Σy = 363, Σx² = 413, Σy² = 13,289, and Σxy = 2137.

(a)Find Se. (Round your answer to three decimal places.)

(b) Find a 90% confidence interval for the annual salary of an individual with x = 5 job changes. (Round your answers to two decimal places.)

1) lower limit

2) upper limit

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

(l) Find a 90% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

1) lower limit

2) upper limit

Answer 1

	n=	10.0000
	X̅=ΣX/n	5.7000
	Y̅=ΣY/n	36.3000
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	3.1287
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	3.5292
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	7.5444
	r=Cov/(Sx*Sy)=	0.6832
	slope= β̂1 =r*Sy/Sx=	0.7707
	intercept= β̂0 ='y̅-β1x̅=	31.9069

a)

Se =√(SSE/(n-2))=

2.733

b)

predicted val=31.907+5*0.771=

35.76

standard error of PI=s*√(1+1/n+(x0-x̅)2/Sxx)=		2.8740
for 90 % CI value of t =	1.860
margin of error E=t*std error   =		5.344
lower confidence bound=xo-E =		30.42
Upper confidence bound=xo+E=		41.10

c)

t=r*(√(n-2)/(1-r2))=	2.647
critical t =	1.860

d)

l)

std error of slope =se(β1) =s/√Sxx=		0.2912
for 90 % CI value of t =	1.860
margin of error E=t*std error   =		0.542
lower confidence bound=xo-E =		0.229
Upper confidence bound=xo+E=		1.312