A Sample of 30 Cookies Is Taken to Test the Claim

question 28

Essay

A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips.The average number of chocolate chips per cookie in the sample was 7.8 with a standard deviation of 3.
a.
State the null and alternative hypotheses.
b.
Using the critical value approach, test the hypotheses at the 5% level of significance.
c.
Using the p-value approach, test the hypotheses at the 5% level of significance.
d.
Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.

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Definitions:

Loaded Question

A question that contains a controversial or unjustified assumption, making it difficult to answer without bias.

Begging the Question

Begging the question is a logical fallacy where the conclusion of an argument is assumed in one of its premises, essentially arguing in a circle without providing proof.

Independent Premises

Arguments or statements that support a conclusion but do not rely on each other to do so.

Fallacy of Division

This logical fallacy assumes that what is true of a whole must also be true of its parts. For example, assuming that because a car is heavy, each part of the car must also be heavy.