All Fresh Seafood is a wholesale fish company based on the east coast of the U.S....

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). 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.

Table #9.2.5: Wholesale Prices of Fish in Dollars

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

Expert Solution

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 <   0

Level of Significance ,    α =    0.05

Sample #1   ---->   east coast
mean of sample 1,    x̅1=   24.10
standard deviation of sample 1,   s1 =    8.17
size of sample 1,    n1=   9

Sample #2   ---->   west coast
mean of sample 2,    x̅2=   21.66
standard deviation of sample 2,   s2 =    5.59
size of sample 2,    n2=   9

difference in sample means =    x̅1-x̅2 =    24.1022   -   21.7   =   2.45

pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    7.0024
std error , SE =    Sp*√(1/n1+1/n2) =    3.3009

t-statistic = ((x̅1-x̅2)-µd)/SE = (   2.4456   -   0   ) /    3.30   =   0.741

Degree of freedom, DF=   n1+n2-2 =    16

p-value =        0.7652 [ excel function: =T.DIST(t stat,df) ]

Conclusion:    p-value>α , Do not reject null hypothesis

There is not enough evidence  to show that a west coast fish wholesaler is more expensive than an east coast wholesaler

orchestra answered 1 year ago

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All Fresh Seafood is a wholesale fish company based on the east coast of the U.S....

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