Question

All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices from both companies for specific fish types ("Seafood online," 2013) ("Buy sushi grade," 2013). Data is in following table:

Fish	All Fresh Seafood Prices	Catalina Offshore Products Prices
Cod	19.99	17.99
Tilapi	6.00	13.99
Farmed Salmon	19.99	22.99
Organic Salmon	24.99	24.99
Grouper Fillet	29.99	19.99
Tuna	28.99	31.99
Swordfish	23.99	23.99
Sea Bass	32.99	23.99
Striped Bass	29.99	14.99

Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level.

(i) Let ?₁= mean wholesale prices from east coast fishery. Let ?₂ = mean wholesale prices from west coast fishery . Which of the following statements correctly defines the null hypothesis H_O?

A.  ?₁ ? ?₂ > 0 (?_d> 0).   B.  ?₁ – ?₂= 0 (?_d= 0) C.  ?₁ – ?₂ < 0  (?_d< 0)   D.  ?₁ + ?₂= 0

(ii) Let ?₁= mean wholesale prices from east coast fishery. Let ?₂ = mean wholesale prices from west coast fishery . Which of the following statements correctly defines the alternate hypothesis H_A?

A.  ?₁ ? ?₂ > 0 (?_d> 0)   B.  ?₁ – ?₂= 0 (?_d= 0)   C.  ?₁ – ?₂ < 0  (?_d< 0) D.  ?₁ + ?₂= 0

(iii) Enter the level of significance ? used for this test:

(iv) Determine sample mean of differences x??div  Determine sample mean of differences  x¯d

(v) Determine sample standard deviation of differences s_d

(vi) Calculate and enter test statistic

(vii) Determine degrees of freedom for the sample of differences df_d:

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

(ix) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?  

A. Reject H_o   B. Fail to reject H_o C. Accept H_o   D. Accept H_A

(x) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.

B. The result is not statistically significant at .05 level of significance. There is not enough evidence to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.

C. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.

D. The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.

Answer 1

(i)

Correct option:

A.      ()

(ii)

Correct option:

C.            ()

(iii)

= 0.05

(iv)

From the given data, the following statistics are calculated:

n1 = 9

1 = 24.1022

s1 = 8.1741

n2 = 9

2= 21.6567

s2= 5.5902

So,

(v)

(vi)

Test statistic is given by:

t = 2.4455/3.3010

= 0.7408

(vii) dfd = n1 + n2 - 2 = 9 + 9 - 2 = 16

(viii) By Technology, P - Value = 0.2348

(ix)

Correct option:

B.   Fail to reject H0.

(x)

B.   The result is not statistically at .05 level of significance. There is not enough evidence to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.