Question

QUESTION 4 (3 points) A sales manager for an adve of contacts and the amount of the sales. To verify this believe, the following data was collected rtising agency believes there is a relationship between the number Number of Salesperson Contacts. Sales lin thousands 12 20 28 4 80 23 85 120 110 10 What is the 95% confidence interval for sales (in thousands) for someone who made 30 contacts? A. 51.5 to 55.8 B. 51.4 to 55.9 C. 46.7 to 60.6 D. 311 to 76.2 E. 71.1 to 85.0 F. None of these answer

Answer 1

right choice is C. 46.7 to 60.6

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.975362
R Square	0.951331
Adjusted R Square	0.945248
Standard Error	9.310446
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	13555.42	13555.42	156.3768	1.56E-06
Residual	8	693.4752	86.6844
Total	9	14248.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-12.201	6.560	-1.860	0.100	-27.327	2.925
X	2.195	0.176	12.505	0.000	1.790	2.599

y=-12.201+2.195x

for x=30, y=-12.201+2.195*30=53.649

confidence interval=53.649$\pm$2.306*9.310*sqrt(1/10+(30-33.4)*(30-33.4)/2814.4)=53.649$\pm$6.927=(46.722, 60.576)~(46.7,60.6)

Confidence interval for the conditional mean of the response variable corresponding to S.x with df n -2 W1