Question

Statistical Analysis: Correlation and Descriptive Statistics

Write results in APA Format.

Sleep blks	Sleep Qual	# correct
36	5	4
48	7	13
43	7	12
32	7	12
38	7	11
44	5	11
58	5	11
54	6	9
45	5	6
27	7	12
54	4	11
38	4	8
27	5	10
42	5	6
38	6	10
48	5	13
54	7	11
45	8	10
60	6	5
56	7	8
48	6	10
50	7	12
60	7	6
45	5	5
43	5	5
43	6	8
33	5	7
51	8	12
37	10	5
51	6	8
54	7	13
45	6	11
48	7	10
63	7	9
54	7	8
46	6	10
30	9	10
48	10	7

Answer 1

here number of observations n=38 and correlation matrix

	Sleep blks	Sleep Qual	# correct
Sleep blks	1
Sleep Qual	0.009187085	1
# correct	-0.008826377	0.10506868	1

here we want to test the correlation coefficient Sleep blks and Sleep Qual.

r=0.0092 ( four decimal place approximation)

Null hypothesis H0:ρ=0 and

Alternate hypothesis Ha: ρ ≠ 0

and we use t-test to test the above pair of hypothesis and

statistic t =r/sqrt[(1—r²)/(n—2)] =0.0092/sqrt((1-0.0092*0.0092)/(38-2))=0.0552 with n-2=38-2=36 degree of freedom(df)

the typical two tailed critical t(0.05,36)=2.0281 is more than calculated t=0.0552 so we fail to reject H0 and conclude that there is 0 correlation between sleep blks and sleep qual.