a calculate the correlation coefficent between the magnitude

a. calculate the correlation coefficent between the magnitude of the increase in slow wave sleep and the magnitude of the improvement in performance upon waking?

b. what is the standard error for your estimate in part a?

c. provide an interpretation of the quantity you calculated in part b. what does it measure?

d. test the hypothesis that the two variables are correlated in the population?

e. is this an observational or experimental study? Explain?

upon waking. ncrease in slow-wave Improvement in task sleep (%) performance (96) 14 13 15 17 18 31 32 15 14 10 27 26 54

Solution

a. calculate the correlation coefficent between the magnitude of the increase in slow wave sleep and the magnitude of the improvement in performance upon waking?

> 0.863

b. what is the standard error for your estimate in part a?

> 8.083

c. provide an interpretation of the quantity you calculated in part b. what does it measure?

> The standard error measures the accuracy of predictions. the smaller the standard error is the higher the chance of predictions being accurate.

d. test the hypothesis that the two variables are correlated in the population?

> Since the Significance F is much smaller value. The null hypothesis can be rejected. Thus the two variables are correlated in this example.

e. is this an observational or experimental study? Explain?

> This is an experimental study since some specific activity is being done and we are checking the effect of that activity. We are not just observing here.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.863321682
R Square	0.745324326
Adjusted R Square	0.713489867
Standard Error	8.083133314
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1529.703647	1529.704	23.4125	0.00129
Residual	8	522.6963534	65.33704
Total	9	2052.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9.539054038	4.027680164	2.368374	0.045361	0.251207	18.8269	0.251207	18.8269
Improvement in task Performance	1.356841979	0.280417661	4.838647	0.00129	0.710198	2.003486	0.710198	2.003486