A sewage treatment plant located along a river reported a chemical spill which may have released...

A sewage treatment plant located along a river reported a chemical spill which may have released mercury into the river. The local environmental regulatory agency requires that such spills be monitored, and any spill that results in a long term mercury level above 2.5 µg/L (micrograms per litre) requires the party at fault to pay a large fee. A random sample of 58 measurements showed a mercury reading near the treatment plant to have a sample mean of 2.7 µg/L with a sample standard deviation of 0.89 µg/L. To decide if they should pay the fee, the treatment plant performs a hypothesis test.

(a) [2 marks] Define the parameter of interest using the correct notation. Then, state the null and alternative hypotheses for this study.

(b) [1 mark] Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.

(c) [1 mark] Compute the p-value or provide a range of appropriate values for the p-value.

(e) [1 mark] Using the significance level α = 0.025, state your conclusions about if the treatment plant will pay the fee.

(f) [1 mark] Using the specifics of this question (but not necessarily your conclusion from part (d)), describe what would happen if a Type I error is made.

(d) [1 mark] Using your p-value, state the strengh of evidence against H0.

Expert Solution

orchestra answered 1 year ago

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