In: Statistics and Probability
Please show your work
9.2.3
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 |
Ho : µd ≤ 0
Ha : µd > 0
SAMPLE 1 | SAMPLE 2 | difference , Di =sample1-sample2 | (Di - Dbar)² |
19.99 | 17.99 | 2 | 0.199 |
6 | 13.99 | -7.99 | 108.901 |
19.99 | 22.99 | -3 | 29.654 |
24.99 | 24.99 | 0 | 5.981 |
29.99 | 19.99 | 10 | 57.070 |
28.99 | 31.99 | -3 | 29.654 |
23.99 | 23.99 | 0 | 5.981 |
32.99 | 23.99 | 9 | 42.961 |
29.99 | 14.99 | 15 | 157.614 |
mean of difference , D̅ =ΣDi / n =
2.4456
std dev of difference , Sd = √ [ (Di-Dbar)²/(n-1) =
7.3994
std error , SE = Sd / √n = 7.3994 /
√ 9 = 2.4665
t-statistic = (D̅ - µd)/SE = ( 2.445555556
- 0 ) / 2.4665
= 0.992
Degree of freedom, DF= n - 1 =
8
t-critical value , t* =
1.8595 [excel function: =t.inv(α,df) ]
p-value = 0.1752 [excel
function: =t.dist.rt(t-stat,df) ]
Decision: p-value>α , Do not reject null
hypothesis