Question

A student in Nampa ranks 10 pizza restaurants based on taste (1 = best tasting) and also on cost (1 = most expensive).

Calculate correlation on the data. Test significance – Is taste positively correlated with cost? Test at alpha = .05.

Taste Rank	Cost Rank
1	1
2	5
3	6
4	2
5	3
6	4
7	10
8	8
9	7
10	9

What is r?

What is r²?

What is the correlation of alienation?

Answer 1

we will perform Spearman's Rank correlation for no tie case:

calculations:

Now Spearman's Rank correlation is

here, n=10

and from the above table:

r=0.733=the sample correlation

r²=0.537289

Correlation test:H₀:=0 ag. H₁:

is the population correlation.

the test statistics is

T is distributed as t distribution with degrees of freedom (n-2)=(10-2)=8

r=0.733

n=10

T=3.0508

tabulated value of t at level with df 8 is

t_0.05;8=1.860

As T>t_0.05;8 or, the test statistic is greater than the tabulated value at level 0.05 So we can reject the null hypothesis and can conclude that Taste is positively related to cost.