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2. Imagine a lead study that...

2. Imagine a lead study that shows elevated soil contamination in neighborhoods near a highway (historical source of lead is gasoline additive). Test a research hypothesis that data (Sample) that was drawn from this same area (Population) is different in its lead contamination, and is therefore not representative. Use a Z-test at the 0.05 level of significance. Write answers to each of the following steps on the answer sheet.

Population HWY Neighborhood Sample

Mean 111 ppm 310 ppm

std dev or s 27 ppm 32 ppm

n N/A 35

a. State your null and alternate hypotheses (H0 and H1). A good rule of thumb is that the null hypothesis has an “=” sign. Also, this will be non-directional since we are trying to show that the sample is representative of the population, and not that it is either greater or less than the population.

b. Identify your test statistic (Z in this case) and your significance level ( =.0.05 in this case). (The answer is easy – simply write down Z and =.0.05 .)

c. Find the critical values of your test statistic (from the table of Z), and state the decision rule (i.e., delineate the regions of rejection and nonrejection of the null hypothesis). Since this is a two-tail test, you will have + and critical values.

d. Calculate the test statistic (a Z-score in this case).

i. Why is Z-score used, rather than t?

Population HWY Neighborhood Sample

Mean 111 ppm 310 ppm

std dev or s 27 ppm 32 ppm

n N/A 35

a. State your null and alternate hypotheses (H0 and H1). A good rule of thumb is that the null hypothesis has an “=” sign. Also, this will be non-directional since we are trying to show that the sample is representative of the population, and not that it is either greater or less than the population.

b. Identify your test statistic (Z in this case) and your significance level ( =.0.05 in this case). (The answer is easy – simply write down Z and =.0.05 .)

c. Find the critical values of your test statistic (from the table of Z), and state the decision rule (i.e., delineate the regions of rejection and nonrejection of the null hypothesis). Since this is a two-tail test, you will have + and critical values.

d. Calculate the test statistic (a Z-score in this case).

i. Why is Z-score used, rather than t?

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