Solve the Problem Do the Data Provide Sufficient Evidence to Support the Claim

question 46

Essay

Solve the problem.
-The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million
(ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained
from one producer. The levels, in ppm, are shown below. $$\begin{array} { l l l l l } 0.31 & 0.47 & 0.19 & 0.72 & 0.56 \\0.91 & 0.29 & 0.83 & 0.49 & 0.28 \\0.31 & 0.46 & 0.25 & 0.34 & 0.17 \\0.58 & 0.19 & 0.26 & 0.47 & 0.81\end{array}$$ Do the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes
from this producer is greater than the recommended level of 0.4 ppm? Use a 0.05 significance level to test the
claim that these sample levels come from a population with a mean greater than 0.4 ppm. Use the P-value
method of testing hypotheses. Assume that the standard deviation of levels of the chemical in all such tomatoes
is 0.21 ppm.

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Definitions:

Self-efficacy

A person's confidence in their ability to carry out actions required to achieve certain performance goals.

Self-appraisal

The process of evaluating one's own behavior, abilities, and qualities, often in relation to certain standards or expectations.

Narcissism

A personality trait characterized by an excessive preoccupation with oneself and a lack of empathy for others.

Self-esteem

The subjective evaluation or perception of one's own worth or value.