Bonus Project 1

Are the fish in the rivers and lakes by Grassy Narrows First Nation safe to eat now?

Purpose

Insert core learning outcomes here.

Resources

Original Source Assignment and Attribution: Grassy Narrows and Muskrat Falls Dam Hypothesis Testing and t-Tests

Tasks

Preliminary

Understand the problem by reading or skimming through the information on the background information pages.

Use the data in Table 1: Mercury Concentration in a fictitious population of Bass in Separation Lake with a mean of 0.5 mg/kg to complete the tasks below.

Demonstration

Create a submission that addresses all the tasks below. Your submission may be in any format.

Distribution of 30 Mean Concentration Levels of Samples
1. Go to the Rossman One Variable with Sampling applet (found hereLinks to an external site.). Clear out existing data and paste in all entries from column A of the spreadsheet. You should have the word "Concentration" at the top, followed by 100 concentration levels of mercury in fish. Click "Use Data" and confirm that the 100 concentrations are displayed in the histogram below.
2. Click "Show Sampling Options" and set the applet to take 30 samples, each with a sample size of 5. Then click "Draw Samples."
3. Take a screenshot of the resulting Histogram on the far right. This graph depicts the sample mean of each of the 30 samples of 5 concentration levels you just collected.
Empirical Probabilities
Calculate each of the following using your histogram or data.
1. The empirical proportion of samples that have means above 2 mg/kg, or $LaTeX: P\left(\overline{x}>2\right)$ .
2. The empirical proportion of samples that have means above 0.6 mg/kg, or $LaTeX: P\left(\overline{x}>0.6\right)$ .
3. The empirical proportion of samples that have means above 0.3 mg/kg, or $LaTeX: P\left(\overline{x}>0.3\right)$ .
4. The sample mean that separates the bottom 95% from the top 5% of observed means, or value of k such that $LaTeX: P\left(\overline{x}>k\right)=0.05$ .
Sampling Distribution of the Mean Concentration in Samples
Use Stapplet to create a sampling distribution of all theoretical sample means assuming the null hypothesis ( $LaTeX: \mu=0.5$ ) is true with a population standard deviation estimated to be $LaTeX: \sigma=0.17$ . Call this chart "Sampling Distribution of the Mean Mercury Concentration in Samples of 5 fish in Separation Lake." Use an x-axis label "Average Mercury Level in Samples (mg/kg)."
Theoretical Probabilities
Using the sampling distribution from task 3, determine each of the following:
1. The theoretical probability of selecting a sample of five fish with a mean above 2 mg/kg, or $LaTeX: P\left(\overline{x}>2\right)$ .
2. The theoretical probability of selecting a sample of five fish with a mean above 0.6 mg/kg, or $LaTeX: P\left(\overline{x}>0.6\right)$ .
3. The theoretical probability of selecting a sample of five fish with a mean above 0.3 mg/kg, or $LaTeX: P\left(\overline{x}>0.3\right)$ .
4. The sample mean that separates the bottom 95% from the top 5% of all means, or value of k such that $LaTeX: P\left(\overline{x}>k\right)=0.05$ .
Analysis
If the healthy limit of mercury is set at 0.5 mg/kg, what is your recommendation on whether or not fish from this population are safe to eat? Provide evidence and reasoning; use previous answers, if possible.

Criteria for Success

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