Question

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.

Distance to Work (miles)	Number of Days Absent
1	8
3	5
4	8
6	7
8	6
10	3
12	5
14	2
14	4
18	2

Using Excel Data Analysis, find the value of the test statistic. (Round your answer to two decimal places.)

Use the estimated regression equation (Y-hat = 8.098 + -0.344X) to develop a 95% confidence interval for the expected number of days absent for employees living 7 miles from the company. (Round your answers to one decimal place.)

_______Days to _______ Days

Answer 1

applying regression on above data:

Source	SS	df	MS	F	p-value
Regression	32.6993	1	32.6993	19.67	.0022
Residual	13.3007	8	1.6626
Total	46.0000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	8.0978	0.8088	10.012	8.41E-06	6.2327	9.9630
x	-0.3442	0.0776	-4.435	.0022	-0.5232	-0.1652
Predicted values for: y
		95% Confidence Interval		95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
7	5.688	4.682	6.695	2.549	8.827	0.114

a)

value of the F test statistic =19.67

and value of the t test statistic =-4.43

b)

95% confidence interval for the expected number of days absent for employees living 7 miles

=(4.7 Days to 6.7 Days)