"Red tide" is a bloom of poison-producing algae-a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds $800\mathrm{\mu g}$(micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. Describe both a Type$\mathrm{I}$ and a Type $\mathrm{II}$error in this context, and state which error has the greater consequence.

Step by step solution

01

Introduction

When the null hypothesis is true, a type one error is defined as rejecting it.

When the null hypothesis is incorrect, a type two mistake occurs when the null hypothesis is not rejected.

02

Explanation

Type$\mathrm{I}$error is,

We believe that the average toxin level in clams does not exceed$800$micrograms per kilogramme of clam meat when, in fact, it does.

Type$\mathrm{II}$error is,

We believe that the mean level of toxicity in clams is greater than $800$micrograms per kilogramme of clam meat when, in fact, it is not.

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