ARandomization Distribution for Arsenic in Chicken Arestaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb , so we are testing $$ H_{0}: \mu=80 \mathrm{vs} H_{a}: \mu80 $$, where $$ \mu $$ represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of $$ n=6 $$ chickens from one supplier is tested, and the resulting sample mean is $$ \bar{x}=91 $$. Subtracting 11 from the sample data to move the mean down to the null mean of $$ \bar{x}=80 $$ results in the following data: Click here to access StatKey. Part 1 (a) Use StatKey or other technology to create the randomization distribution for this test. Find the $$ p $$-value. Round your answer to three decimal places. Use 1000 samples. p-value $$ = $$ i

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ARandomization Distribution for Arsenic in Chicken Arestaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb , so we are testing $$ H_{0}: \mu=80 \mathrm{vs} H_{a}: \mu>80 $$, where $$ \mu $$ represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of $$ n=6 $$ chickens from one supplier is tested, and the resulting sample mean is $$ \bar{x}=91 $$. Subtracting 11 from the sample data to move the mean down to the null mean of $$ \bar{x}=80 $$ results in the following data: Click here to access StatKey. Part 1 (a) Use StatKey or other technology to create the randomization distribution for this test. Find the $$ p $$-value. Round your answer to three decimal places. Use 1000 samples. p-value $$ = $$ i

UpStudy AI · Accepted Answer

To solve this problem, we need to create a randomization distribution for the hypothesis test and find the $$ p $$-value. Here’s how we can approach it step by step:

### Step 1: Understand the Hypothesis Test
We are testing the following hypotheses:
- Null Hypothesis ($$ H_0 $$): $$ \mu = 80 $$ ppb
- Alternative Hypothesis ($$ H_a $$): $$ \mu > 80 $$ ppb

### Step 2: Gather Sample Data
From the problem, we have:
- Sample size ($$ n $$) = 6
- Sample mean ($$ \bar{x} $$) = 91 ppb

### Step 3: Create the Randomization Distribution
To create the randomization distribution, we will:
1. Randomly sample from a distribution where the mean is equal to the null hypothesis (80 ppb).
2. Calculate the mean of each sample.
3. Repeat this process 1000 times to create a distribution of sample means.

### Step 4: Calculate the $$ p $$-value
The $$ p $$-value is the proportion of random samples that have a mean greater than or equal to the observed sample mean (91 ppb).

### Step 5: Use Technology
Since I cannot directly access StatKey or other software, I will guide you on how to do it:

1. **Open StatKey**: Go to the randomization distribution section.
2. **Set the Null Hypothesis Mean**: Input 80 as the mean for the null hypothesis.
3. **Input Sample Size**: Set the sample size to 6.
4. **Generate Random Samples**: Click to generate 1000 random samples.
5. **Calculate the Sample Means**: StatKey will provide you with a distribution of sample means.
6. **Find the $$ p $$-value**: Look for the proportion of sample means that are greater than or equal to 91.

### Final Step: Report the $$ p $$-value
Once you have completed the above steps in StatKey, you will find the $$ p $$-value. Round this value to three decimal places and report it.

If you have access to the software and can perform these steps, please let me know the resulting $$ p $$-value, and I can help you interpret the results!
To determine if the mean arsenic level is greater than 80 ppb, create a randomization distribution with 1000 samples of size 6, set the null mean to 80 ppb, and calculate the $$ p $$-value as the proportion of sample means ≥ 91 ppb. Round the $$ p $$-value to three decimal places.

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