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 3 76 3 4 72 4 6 77 5 8 92 6 8 109 7 9 126 8 9 122 9 10 124 10 11 120 The data on  annual sales  for new customer accounts and  number of years of experience for a sample of  salespersons provided the estimated regression equation . For these data , , and . a. Develop the  confidence interval for the mean annual sales for all salespersons with seven years of experience. ( ,  ) (to 2 decimals) b. The company is considering hiring Tom Smart, a salesperson with seven years of experience. Develop a  prediction interval of annual sales for Tom Smart. ( ,  ) (to 2 decimals) c. Discuss the differences in your answers to parts (a) and (b). As expected, the prediction interval is much - Select your answer -widernarrowItem 5 than the confidence interval. This is due to the fact that it is more - Select your answer -difficulteasyItem 6 to predict annual sales for one new salesperson with 7 years of experience than it is to estimate the mean annual sales for all salespersons with 7 years of experience.

Answer 1

a)

Answer:

Explanation:

To calculate the confidence interval, the regression analysis is done in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Y' column, Input X Range: 'X' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

The standard error of the regression is,

For X = 7,

Now, the confidence interval for the predicted value for x = 7 is obtained using the formula

From the data values,

	x	x^2
	1	1
	3	9
	4	16
	6	36
	8	64
	8	64
	9	81
	9	81
	10	100
	11	121
Sum	69	573

The t-critical value is obtained from t-distribution table for significance level = 0.05 and degree of freedom = n - 2 = 8

b)

Answer:

Explanation:

The prediction interval for the predicted value for x = 7 is obtained using the formula,

c)

Answer:

As expected, the prediction interval is much wider than the confidence interval. This is due to the fact that it is more difficult to predict annual sales for one new salesperson with 7 years of experience than it is to estimate the mean annual sales for all salespersons with 7 years of experience

Explanation:

The prediction interval is always wider than the confidence interval as the prediction interval predict the value for the next expected value.