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??d{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathsize="14px"><mrow><mfenced><mi mathvariant="bold">iv</mi></mfenced><mo mathvariant="bold">&#xA0;</mo><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">Determine</mi><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">sample</mi><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">mean</mi><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">of</mi><mo mathvariant="bold">&#xA0;</mo><mi mathvariant="bold">differences</mi><mo mathvariant="bold">&#xA0;</mo><mo mathvariant="bold">&#xA0;</mo><msub><mover><mi mathvariant="bold">x</mi><mo mathvariant="bold">&#xAF;</mo></mover><mi mathvariant="bold">d</mi></msub></mrow></mstyle></math>"}

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.

Answer 1

Matched paired test:

1) Null hypothesis: Mean difference equal to zero

2) Alternate hypothsis: Mean difference is greaterthan zero

3) Significant level= 0.05

4)

All	Catalina	diff
19.99	17.99	-2
6	13.99	7.99
19.99	22.99	3
24.99	24.99	0
29.99	19.99	-10
28.99	31.99	3
23.99	23.99	0
32.99	23.99	-9
29.99	14.99	-15
	Mean diff	-2.44556
	Std diff	7.399438

Mean= -2.44556

5) standard deviation= 7.399438

6)The test statistic:

7) The degree of freedom= n-1=8

8) P-value:0.175236

9) Fail to reject H0: becasue p-value >0.05

10) 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