Question

Washington State law says dissolved oxygen in marine waters must not be less than 5 m/L. The Washington Department of Ecology uses their Salish Sea model to predict the concentration of dissolved oxygen in the Puget Sounds at any given place and time to see where dissolved oxygen is below the 5 mg/L threshold. Their reported standard deviation around this prediction is 1 mg/L. What value of dissolved oxygen must their model predict in order to be 95% confident that the true value is in fact below the threshold? Repeat for 80% confidence. What are your assumptions?

Answer 1

Since there is no mention of number of samples collected and it is very important to know this value for calculations, I am assuming the number of samples to be at least 30 which makes the samples good representative of population. I hope the first line says 5mg/L instead of 5m/L.

Therefore, the only assumption I have taken is :

1. Sample size is at least 30.

In the first line in the below image, we know the z-score for 95% Confidence Interval from z-table.