Lead (Pb) concentrations were measured in waterfowl eggshell samples from two locations. In n1 = 41 samples from a location downstream from a paper mill, the mean Pb concentration was 1 x = 0.13 ppm with a standard deviation of s1 = 0.04 ppm. In n2 = 31 samples from a location upstream from the paper mill, the PB concentration was 2 x = 0.09 ppm with a standard deviation of s2 = 0.05 ppm. Test the hypothesis of no difference in mean Pb eggshell concentrations versus the alternative that the locations downstream from the papermill have a higher mean Pb concentration. Use a 1% level of significance.

Question

Lead (Pb) concentrations were measured in waterfowl eggshell samples from two locations. In n1 = 41 samples from a location downstream from a paper mill, the mean Pb concentration was 1 x = 0.13 ppm with a standard deviation of s1 = 0.04 ppm. In n2 = 31 samples from a location upstream from the paper mill, the PB concentration was 2 x = 0.09 ppm with a standard deviation of s2 = 0.05 ppm. Test the hypothesis of no difference in mean Pb eggshell concentrations versus the alternative that the locations downstream from the papermill have a higher mean Pb concentration. Use a 1% level of significance.

Answer 1

Try a two-sample z-test.

Hypotheses:
Ho: µ1 = µ2
Ha: µ1 > µ2

Use a z-table to determine the critical or cutoff value to reject or fail to reject the null hypothesis at .01 level of significance. This will be a one-tailed test because the alternative hypothesis is showing a specific direction. Keep that in mind when you are looking at the value in the table.

Once you have the value from the table, compare to the test statistic. If the test statistic exceeds the value from the table, reject the null and conclude µ1 > µ2. If the test statistic does not exceed the value from the table, fail to reject the null and you cannot conclude a difference.

I hope this will help get you started on your problem.