Question

1. Listed below are the temperatures from nine males measured at 8 AM and again at 12 AM.

(a) Construct a scatter plot.

(b) Find the coefficient of correlation and corresponding p value.

(c) Based on the graph, does there appear to be a relationship between 8 AM temperatures and 12 AM temperatures? How significant is this relationship? State the null hypothesis and accept or reject it. Give your reason for the decision.

8 AM	12 AM
98.0	98.0
97.0	97.6
98.6	98.8
97.4	98.0
97.4	98.8
98.2	98.8
98.2	97.6
96.6	98.6
97.4	98.6

At least how many values are two standard deviations away from the mean if

(d) the distribution is normal? (e) the distribution is skewed?

Answer 1

a)

b)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
98	98	0.1264	0.0968	-0.1106
97	97.6	0.4153	0.5057	0.4583
98.6	98.8	0.9131	0.2390	0.4672
97.4	98	0.0598	0.0968	0.0760
97.4	98.8	0.0598	0.2390	-0.1195
98.2	98.8	0.3086	0.2390	0.2716
98.2	97.6	0.31	0.51	-0.40
96.6	98.6	1.09	0.08	-0.30
97.4	98.6	0.06	0.08	-0.07

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	878.80	884.80	3.34	2.09	0.28
mean	97.64	98.31	SSxx	SSyy	SSxy

sample size ,   n =   9          
here, x̅ = Σx / n=   97.644   ,     ȳ = Σy/n =   98.311  
                  
SSxx =    Σ(x-x̅)² =    3.3422          
SSxy=   Σ(x-x̅)(y-ȳ) =   0.3          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.1043

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   9  
alpha,α =    0.05  
correlation , r=   0.1043  
t-test statistic = r*√(n-2)/√(1-r²) =        0.277
DF=n-2 =   7  
p-value =    0.7895  
Decison:   P value > α, So, Do not reject Ho  

c)

there does not appear to be a relationship between 8 AM temperatures and 12 AM temperatures

relationship is not significant.

because P value =0.7895 > α, So, Do not reject Ho