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 west coast fishery. Let ?₂ = mean wholesale prices from east 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

Enter letter corresponding to correct answer

(ii) Let ?₁= mean wholesale prices from west coast fishery. Let ?₂ = mean wholesale prices from east 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

Enter letter corresponding to correct answer

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

Enter in decimal form. Examples of correctly entered answers:  0.01    0.02    0.05    0.10

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

Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers:  

0.0001

0.0020

0.3000

11.2485

(v) Determine sample standard deviation of differences s_d

Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers:  

0.0001    0.0020     0.0500      0.3000   0.5115

(vi) Calculate and enter test statistic

Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers:

–2.0104      –0.3070        +1.6000        +11.0019

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

Enter value in integer form. Examples of correctly entered answers:

2    5    9    23    77

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

Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143    1.0000

(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

Enter letter corresponding to correct answer.

  (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.

Show Work

Answer 1

The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the alternate hypothesis.

The alternative hypothesis is usually taken to be that the observations are the result of a real effect. It is what we want to check to be the truth from the data.

Now we need to check the data for the fact that the mean prices of the west coast fishery ?1 is greater than the mean prices of the east coast fishery ?2 so this becomes our alternate hypothesis.
?1 > ?2 or
?1 - ?2 > 0 (?d > 0)

So the Null hypothesis being opposite of the alternative hypothesis becomes
?1 - ?2 < 0 (?d < 0)

i)
H0 becomes
?1 - ?2 < 0 (?d < 0)

ii)
HA becomes
?1 - ?2 > 0 (?d > 0)

iii)
It is given that we have to test at 5% level.
So, the level of significance = 5% = 5/100
= 0.05 (in decimal form)

iv) To calculate the sample mean of differences we subtract prices of east coast from the prices of west coast for individual fish. (while preserving the sign)
For example, for cod fish we subtract prices of east coast from the prices of west coast to get 17.99-19.99 = -2.00
Similarly we find the difference of all fish types given in the below table.

Now we find the sample mean of the calculated data.
For that, we take a sum of all the difference and divide by the number of fishes( = 9)

So, the sample mean of differences = -22.01/9 = -2.4455556