### Question 3 (1 point)**Mercury in Tuna** ~ Mercury, if ingested, can cause severe health problems. The amount of mercury in Tuna’s body tissue is much higher than other fish.It is known that the amount of mercury in Albacore tuna is normally distributed with a mean of 10.13 micrograms and a standard deviation of 2.03 micrograms per ounce.A food company has a production line for canned albacore tuna. They regularly take random samples of 10 cans of tuna and test the amount of mercury. If the sample mean amount of mercury in tuna exceeds 12 micrograms per ounce, the production line will be stopped to find the source of contamination.Let μ denote the actual population mean amount of mercury in tuna per ounce. The hypotheses for this testing situation are:\[ H_0: \mu = 10.13 \]\[ H_A: \mu > 10.13 \]What is the chance of making a Type I error using the decision rule given above? Give your answer to 4 decimal places.**Your Answer:**[Text Box for Answer]### Explanation- **Type I Error**: A Type I error occurs when the null hypothesis (H0) is true, but we incorrectly reject it.- **Decision Rule**: The decision rule in this scenario is to stop the production if the sample mean mercury level exceeds 12 micrograms per ounce. - **Hypotheses**: - Null Hypothesis ($ H_0 $): The mean amount of mercury is 10.13 micrograms per ounce. - Alternative Hypothesis ($ H_A $): The mean amount of mercury is greater than 10.13 micrograms per ounce.- **Standard Deviation ($ \sigma $)**: 2.03 micrograms per ounce.- **Sample Size (n)**: 10 cans.To find the probability of making a Type I error (α), calculate the probability that the sample mean exceeds 12 micrograms per ounce assuming the null hypothesis is true.This task involves finding the z-score corresponding to 12 micrograms for the sample mean distribution, and then finding the probability associated with this z-score assuming $ \mu = 10.13 $.\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \]Where:- $ \bar{x} $ =

P(Type I error) =P(rejection of null hypothesis when null hypothesis is true) =P(Rejection of H0 |…

Mercury in Tuna ~ Mercury, if ingested can cause severe health problems. The amount of mercury in Tuna's body tissue is much higher than other fish. It is known that the amount of mercury in Albacore tuna is normally distributed with mean 10.13 micrograms and standard deviation of 2.03 micrograms per ounce. A food company has a production line for canned albacore tuna. They regularly take random samples of 10 cans of tuna and test the amount of mercury. If the sample mean amount of mercury in tuna exceeds 12 micrograms per ounce, the production line will be stopped to find the source of contamination. Let u denote the actual population mean amount of mercury in tuna per ounce. The hypotheses for this testing situation are: Ho : µ = 10.13 vs HA : µ > 10.13. What is the chance of making a Type I error using the decision rule given above? Give your answer to 4 decimal places.

Mercury in Tuna ~ Mercury, if ingested can cause severe health problems. The amount of mercury in Tuna's body tissue is much higher than other fish. It is known that the amount of mercury in Albacore tuna is normally distributed with mean 10.13 micrograms and standard deviation of 2.03 micrograms per ounce. A food company has a production line for canned albacore tuna. They regularly take random samples of 10 cans of tuna and test the amount of mercury. If the sample mean amount of mercury in tuna exceeds 12 micrograms per ounce, the production line will be stopped to find the source of contamination. Let u denote the actual population mean amount of mercury in tuna per ounce. The hypotheses for this testing situation are: Ho : µ = 10.13 vs HA : µ > 10.13. What is the chance of making a Type I error using the decision rule given above? Give your answer to 4 decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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