Question

A researcher suspects that the mean pollutant level in a region is higher than the state average of 4.3 grams/cubic liter. Data are collected; from 56 samples, the mean is found to be 5.4, with a standard deviation of 5.0. Test the null hypothesis that the true mean in the region is 4.3, against the alternative that it is higher. State the null and alternative hypotheses, give the critical value, find the test statistic, make a decision, and give the p-value

Answer 1

Let X:The pollutent level in grams/cubic litre.

To test

vs

given information of sample is

n=56

Critical value at 5% LOS is equal to= 1.64.

Test statistic is given by

The p value is given by

Therfore at 5% LOS we reject the null hypothesis because 0.05>0.049848.

That is we can conclude that at 5% LOS the true mean is higher than 4.3.

Thank you !!