A Sample of 30 Cookies Is Taken to Test the Claim

question 145

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 hypothesis 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:

Assignable Cause

A specific, identifiable source of variation in a process, distinct from random variation and often indicating a need for corrective action.

Inadequate Training

A situation where employees have not been provided sufficient or appropriate training to perform their jobs effectively.

Central Limit Theorem

The theoretical foundation for \(\overline{x}\)-charts, which states that regardless of the distribution of the population of all parts or services, the x distribution tends to follow a normal curve as the number of samples increases.

Normal Distribution

A probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.