Question

A magazine tested LCD televisions. The table below shows the overall quality score and cost in hundreds of dollars. Use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of a=0.05.Based on these​ results, can you expect to get higher quality by purchasing a more expensive LCD​ television?

Quality	75	71	67	64	63	60	57	54	54	53	51	Open in StatCrunch + Copy to Clipboard + Open in Excel +
Cost	21	24	32	19	18	14	21	19	16	14	18

Determine the null and alternative hypotheses for this test.

Determine the correlation coefficient.

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
75	21	201.124	1.860	19.339
71	24	103.669	19.041	44.430
67	32	38.215	152.860	76.430
64	19	10.124	0.405	-2.025
63	18	4.760	2.678	-3.570
60	14	0.669	31.769	4.612
57	21	14.579	1.860	-5.207
54	19	46.488	0.405	4.339
54	16	46.488	13.223	24.793
53	14	61.124	31.769	44.066
51	18	96.397	2.678	16.066

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	669	216	623.636	258.5	223.272727
mean	60.82	19.64	SSxx	SSyy	SSxy

sample size ,n    =11

here,   x̅   =60.82,ȳ =19.636

SSxx = Σ(x-x̅)² = 623.64

SSxy=Σ(x-x̅)(y-ȳ) =223.3

correlation coefficient , r = Sxy/√(Sx.Sy)   =0.5560

correlation hypothesis test

Ho:ρ = 0

Ha:ρ ╪ 0

n=11

alpha,α = 0.05

correlation , r=0.5560

t-test statistic = t = r*√(n-2)/√(1-r²) = 2.0070

p-value = 0.0757    [excel function: =t.dist.2t(2.007,9) ]

p-value >α=0.05, fail to reject null hypothesis

Fail to reject the null hypothesis. There is insufficient evidence to support a claim of a correlation between quality and price