A researcher conducted a test to learn the effect of lead levels in human bodies. He collected the IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The summary of finding is listed below. Use a 0.05 significance level to test the claim that the mean IQ score of people with low lead levels is higher than the mean IQ score of people with high lead levels.

We do not know the values of the population standard deviations.

Low Lead Level .

n₁ 78

xbar1 92.88

s₁ 15.34

High Lead Level

n₂ 21

xbar2 86.9

s₂ 8.99

Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.

Calculate the critical value, the test statistic, and p-value. Show calculations below

Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.