Question

A national study conducted by a market research firm, evaluated the top technology companies and their reputations. The following shows how 10 technology companies ranked in reputation and how the companies ranked in percentage of respondents who said they would purchase the company's stock. A positive rank correlation is anticipated because it seems reasonable to expect that a company with a higher reputation would have the more desirable stock to purchase.

Company	Reputation	Stock Purchase
Company A	1	3
Company B	2	4
Company C	3	1
Company D	4	2
Company E	5	9
Company F	6	5
Company G	7	10
Company H	8	6
Company I	9	8
Company J	10	7

(a) Compute the rank correlation between reputation and stock purchase. (Round your answer to three decimal places.)

r_s =

(b)Test for a significant positive rank correlation.

State the null and alternative hypotheses.

H₀: ρ_s ≥ 0
H_a: ρ_s < 0

H₀: ρ_s ≤ 0
H_a: ρ_s > 0   

H₀: ρ_s > 0
H_a: ρ_s = 0

H₀: ρ_s ≠ 0
H_a: ρ_s = 0

H₀: ρ_s = 0
H_a: ρ_s ≠ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

(c) At α = 0.05, what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant positive rank correlation between a company's reputation and having stock that is desirable to purchase.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant positive rank correlation between a company's reputation and having stock that is desirable to purchase.    

Do not reject H₀. There is sufficient evidence to conclude that there is a significant positive rank correlation between a company's reputation and having stock that is desirable to purchase.

Reject H₀. There is not sufficient evidence to conclude that there is a significant positive rank correlation between a company's reputation and having stock that is desirable to purchase.

Answer 1

(c) Reject H0. There is sufficient evidence to conclude that there is a significant positive rank correlation between a company's reputation and having stock that is desirable to purchase.