Question

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of salespersons. Salesperson Years of Experience Annual Sales ($1000s)

1 1 80

2 2 100

3 3 106

4 4 105

5 6 111

6 8 120

7 9 121

8 11 116

9 13 136

10 14 142

The data y= on annual sales($1000s) for new customer accounts and x= number of years of experience for a sample of 10 salespersons provided the estimated regression equation y=88.22+3.59x . For these data x=7.1, (xi-x)²192.90 , and s=6.8693.

a. Develop the 95% confidence interval for the mean annual sales for all salespersons with twelve years of experience. ( , ) (to 2 decimals)

b. The company is considering hiring Tom Smart, a salesperson with twelve years of experience. Develop a 95% prediction interval of annual sales for Tom Smart. ( , ) (to 2 decimals)

Answer 1

Solution: We can use the excel regression data analysis tool to find the answers to the given questions. The excel output is given below:

Regression Analysis
Regression Statistics
Multiple R	0.9317
R Square	0.8681
Adjusted R Square	0.8516
Standard Error	6.8693
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2484.5997	2484.5997	52.6537	0.0001
Residual	8	377.5003	47.1875
Total	9	2862.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	88.21877	4.12918	21.36471	0.00000	78.69686	97.74067
Years of Experience	3.58891	0.49459	7.25629	0.00009	2.44837	4.72944
For Average Y
Interval Half-Width	7.51
Confidence Interval Lower Limit	123.78
Confidence Interval Upper Limit	138.79
For Individual Response Y
Interval Half-Width	17.53
Prediction Interval Lower Limit	113.76
Prediction Interval Upper Limit	148.81

a. Develop the 95% confidence interval for the mean annual sales for all salespersons with twelve years of experience. ( , ) (to 2 decimals)

Answer:

b. The company is considering hiring Tom Smart, a salesperson with twelve years of experience. Develop a 95% prediction interval of annual sales for Tom Smart. ( , ) (to 2 decimals)

Answer: ​​​​​​​