Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she kept careful records of the number of visits (x) she made each week and the number of people (y) who bought insurance that week. For a random sample of 15 such weeks, thexandyvalues follow.

x	13	20	15	14	28	5	20	14	22	7	15	29	8	25	16
y	5	13	9	3	8	2	5	6	8	3	5	10	6	10	7

In this setting we havex=251,y=100,x²=4939,y²=796, andxy=1892.(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 1% 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) In a week during which Dorothy makes22visits, how many people do you predict will buy insurance from her? (Round your answer to one decimal place.) people (f) FindS_e. (Round your answer to three decimal places.) S_e= (g) Find a 95% confidence interval for the number of sales Dorothy would make in a week during which she made22visits. (Round your answers to one decimal place.)

lower limit	sales
upper limit	sales

(h) Test the claim that the slopeof the population least-squares line is positive at the 1% 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 an 80% confidence interval forand interpret its meaning. (Round your answers to three decimal places.)

lower limit
upper limit

Interpretation

For each additional visit made, sales increase by an amount that falls within the confidence interval.

For each less visit made, sales increase by an amount that falls within the confidence interval.

For each additional visit made, sales increase by an amount that falls outside the confidence interval.

For each less visit made, sales increase by an amount that falls outside the confidence interval.