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 ba

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). 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

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Aaliyah 4 weeks 2021-12-29T08:04:03+00:00 1 Answer 0 views 0

Answers ( )

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    2021-12-29T08:05:22+00:00

    Answer:

    Check the explanation

    Step-by-step explanation:

    This is a Dependent Sample t-test for Difference of Means. We are given subscript 1 and 2 for East and West coast fishery respectively. The hypotheses statements are

    H_{0}:\mu _{1}- \mu _{2}=0~\left ( \mu _{d}=0 \right )~~~H_{A}:\mu _{1}-\mu _{2}<0~\left ( \mu _{d}<0 \right )\textup{ (Left--Tail test)}

    \textup{Given, test is at 5\% level. hence, level of significance, }\alpha =0.05

    We shall use the Student’s t distribution. We assume that d has an approximately normal distribution.

    The statistical analysis of data pairs gives the following values

    Item       AFS (East)           COP (West)       Difference (d        d^2

    Cod                  19.99                 17.99               2              4

    Tilapi              6                         13.99            -7.99          63.8401

    FS           19.99                22.99              -3               9

    OS           24.99                24.99              0 0

    GF           29.99                19.99              10               100

    Tuna   28.99                31.99              -3               9

    Swordfish 23.99                23.99              0 0

    Sea Bass 32.99                23.99              9 81

    SB           29.99                14.99              15               225

                                                                                       22.01          491.8401

    \sum d=22.01,~~\sum d^{2}=491.8401~\textup{ for number of data pairs, }n=9

    \textup{Average of differences, }\overline{d}=\frac{\sum d}{n}=2.445556

    \textup{Sample St. Deviation of differences, }s_{d}=\sqrt{\frac{\sum d^{2}-\frac{(\sum d)^{2}}{n}}{n-1}}

    =\sqrt{\frac{491.8401-\frac{22.01^{2}}{9}}{8}}\approx 7.3994

    \textup{Test statistic, }t=\frac{\overline{d}}{s_{d}/\sqrt{n}}=\frac{2.445556}{7.3994/\sqrt{9}}\approx 0.9915

    \textup{Degrees of freedom for }t-\textup{distribution, }df=n-1=8

    \textup{Using calculator, }p-\textup{value}=\mathbb{P}(t<0.9915)_{df=8}=0.8245

    \textup{Comparing }p-\textup{value and }\alpha \textup{ value, Fail to reject }H_{0}

    Since

    The p-value is bigger than the significance level, therefore we fail to reject the null hypothesis, and will conclude with option B – There is not sufficient evidence to support the claim that west coast fish wholesalers are more expensive than east coast wholesalers.

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