The Texas Department of Natural Resources has issued warnings about oysters take

Question

The Texas Department of Natural Resources has issued warnings about oysters taken from Galveston Bay It has declared that oysters are unsafe to cat if the mean polychlorina biphenol (PCB) concentration is greater than 5 parts per billion (ppb). Curt N Rod owns a local Captain D's. He and his customers may be affected by the results of the department's study He only wants to sell the oysters if the mean PCB level is less than or equal to 5 where they are safe to eat. a) Define the variable of interest and what is the null and alternative hypothesis? b) Describe the effect and consequence of a type 1 error in this case. c) Describe the effect and consequence of a type II error in this ease.

Explanation / Answer

(a) Here the variable of interest is the mean concentration of PCB.
We are more interested in knowing if the mean concentration of PCB is more than 5, if we found evidence to conclude that we can not accept the oysters.

Hence null and alternate hypothesis are
H0: mean <= 5
H1: mean > 5

(b)
Here Type I error would be if we reject the null hypothesis though the actual mean concentration of PCB is less than or equal to 5. This will result into the decision where these oysters will be considered unsafe to eat and will not be used.

(c)
Here Type II error would be if we accept the null hypothesis though actual mean concentration of PCB is greater than 5. This may result into the use oyster for eating though they are unsafe to eat.
This mean type II error is more severe than Type I

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