# Hypotheses testing for a pollutant in a river

The mean level of pollutant in a river is known to be 1.1 mg/L with a standard deviation of 0.16 mg/L.
a) let the random variable X represent the mean level of pollutant in the measurements from a random sample of 25 sites along the river.
Write down the mean and standard deviation of X.

After a chemical spill, the mean level of pollutant from a random sample of 25 sites is found to be 1.2 mg/L. To determine whether this sample provides evidence that the mean level of pollutant has increased, a statistical test is carried out.
b) Write down suitable hypotheses H_0 and H_1 to test whether the mean levelofpollutant has increased.

c) i) Find the p value for this test, correct to four decimal places.
ii) State with a reason whether the sample supports the contention that there has been an increase in the mean level of pollutant after the spill. Test at the 5% level of significance.

d) For this test, what is the smallest value of the sample mean that would provide evidence that the mean level of pollutant has increased? That is, find X such that (see the attachment for full equation). Give your answer correct to three decimal places.

e) Suppose that for a level of significance of 2.5%, we find that (see the attachment for the full equation).

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