The Environmental Protection Agency (EPA) is concerned that the residue being du

Question

The Environmental Protection Agency (EPA) is concerned that the residue being dumped into a river by a manufacturing company is polluting the river with dangerous levels of lead. The amount of lead in a drinking water supply should not exceed 15 parts per billion (ppb). The EPA takes 36 water samples and measures the amount of lead in each. The EPA knows that the population standard deviation for the amount of lead in a sample is 3 parts per billion. At the 5% level of significance, use the data in the Excel spreadsheet to determine if there enough evidence to conclude that the water supply is safe and has lead levels less than 15 parts per billion? a. Explain why a Z-test is appropriate to use here using the variable situation and parameter of interest. b. What are the null and alternative hypotheses? c. Check the conditions to ensure that a Z-test is appropriate to use. d. Calculate the test statistic. e. Calculate the p-value. Show all calculations to receive full credit. f. What is/are the critical value(s) of this test? g. Will you reject or fail to reject the null hypothesis? Explain why using the critical value or p-value h. Write a conclusion in the context of the problem. i. Suppose the average lead level in the river is actually 13 ppb. Did you make a Type Ierror, a Type II error, or the correct decision in part (g)?

Explanation / Answer

here we are checking if lead level are less then 15; hence it is left tailed test.

f )therefore critical value is z= -16449 ( you may use excel ; normsinv(0.05) function to get that

g)as p value is less then 0.05 level; therefore we reejct null hypothesis.

h)we have sufficient evidence to conclude at 0.05 level that water supply is safe and has lead level less than 15 parts per billion.

i) as we have concluded that lead level is less then 15 ppb which is true from correct level; therefore we have made correct decision.

please revert for any clarification

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