Question

1. An industrial plant was trying to determine if hours of training affected the output per week of employees. They randomly sampled 15 employees and randomly assigned them to 5, 9 or 16 hours of training before putting them on the production line. The output of the third week after training was measured and the following data were gathered for the 15 employees.

5	9	16
8	16	23
9	18	26
10	20	26
12	22	29
16	24	26

1. What type of data are these values?
2. Can the results be generalized and can cause and effect statements be made. Explain.
3. What are the independent and independent variables?
4. Do a complete analysis of these data including the two ANOVAs, regression, and confidence intervals.
5. Complete a detailed write-up to the CEO of the firm explaining the impact of training on output and make a recommendation that should be considered at the next board meeting.

Answer 1

1. What type of data are these values?

Quantitative data as all data values are numerical in hours.

1. Can the results be generalized and can cause and effect statements be made. Explain.

Yes because hours of training affect the output per week of employees.

1. What are the independent and independent variables?

The independent variable is 5, 9 or 16 hours of training.

The dependent variable is output per week of employees.

1. Do a complete analysis of these data including the two ANOVAs, regression, and confidence intervals.

	r²	0.903
	r	0.950
	Std. Error	1.140
	n	5
	k	1
	Dep. Var.	9
ANOVA table
Source	SS	df	MS	F	p-value
Regression	36.1000	1	36.1000	27.77	.0133
Residual	3.9000	3	1.3000
Total	40.0000	4
Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	9.5500
5	0.9500	0.1803	5.270	.0133	0.3763	1.5237

	r²	0.200
	r	0.447
	Std. Error	2.191
	n	5
	k	1
	Dep. Var.	16
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3.6000	1	3.6000	0.75	.4502
Residual	14.4000	3	4.8000
Total	18.0000	4
Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	22.7000
5	0.3000	0.3464	0.866	.4502	-0.8024	1.4024

	r²	0.450
	r	0.671
	Std. Error	1.817
	n	5
	k	1
	Dep. Var.	16
ANOVA table
Source	SS	df	MS	F	p-value
Regression	8.1000	1	8.1000	2.45	.2152
Residual	9.9000	3	3.3000
Total	18.0000	4
Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	17.0000
9	0.4500	0.2872	1.567	.2152	-0.4641	1.3641

1. Complete a detailed write-up to the CEO of the firm explaining the impact of training on output and make a recommendation that should be considered at the next board meeting.

From the results above, we can say that there is an impact of 5 & 16 hours of training on output.