A Sample of 16 Cookies Is Taken to Test the Claim

question 7

Essay

A sample of 16 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 7.875 with a standard deviation of 1. Assume the distribution of the population is normal.
a.State the null and alternative hypotheses.
b.Using a critical value, test the hypothesis at the 1% level of significance.
c.Using a p-value, test the hypothesis at the 1% 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:

Comptroller of the Currency

This is a government official responsible for overseeing the federal banking system and ensuring the stability and compliance of national banks.

Lender of Last Resort

A lender of last resort is an institution, usually a country's central bank, that offers loans to banks or other eligible institutions that are experiencing financial difficulty or are considered highly risky.

Federal Reserve

The central banking system of the United States, which regulates banks, manages the country's money supply, and aims to ensure financial stability.

Monetary Policy

The actions undertaken by a central bank, such as the Federal Reserve, to control the money supply and influence the economy's overall level of activity, inflation, and interest rates.