Listed in the data table are IQ scores for a random sample of subjects with medium lead levels in their blood. Also listed are statistics from a study done of $1 Q$ scores for a random sample of subjects with high lead levels. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.
Click the icon to view the data table of $I Q$ scores.
a. Use a 0.05 significance level to test the claim that the mean $1 Q$ scores for subjects with medium lead levels is higher than the mean for subjects with high lead levels.
What are the null and alternative hypotheses? Assume that population 1 consists of subjects with medium lead levels and population 2 consists of subjects with high lead levels.
\[
\begin{array}{l}
H_{0}: \mu_{1}=\mu_{2} \\
H_{1}: \mu_{1} \neq \mu_{2}
\end{array}
\]
\[
\begin{array}{l}
H_{0}: \mu_{1}=\mu_{2} \\
H_{1}: \mu_{1}> \mu_{2}
\end{array}
\]
\[
\begin{array}{r}
H_{0}: \mu_{1} \neq \mu_{2} \\
H_{1}: \mu_{1}> \mu_{2}
\end{array}
\]
\[
\begin{array}{l}
H_{0}: \mu_{1} \leq \mu_{2} \\
H_{1}: \mu_{1}> \mu_{2}
\end{array}
\]
The test statistic is (Round to two decimal places as needed.)
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Answer
Final Answer: The null and alternative hypotheses are: \(\boxed{H_{0}: \mu_{1}=\mu_{2}}\) and \(\boxed{H_{1}: \mu_{1}>\mu_{2}}\)
Step 1 ：The question is asking for the null and alternative hypotheses for a statistical test comparing the mean IQ scores of two populations: those with medium lead levels and those with high lead levels. The claim we are testing is that the mean IQ score for subjects with medium lead levels is higher than the mean for subjects with high lead levels.
Step 2 ：The null hypothesis is typically a statement of no effect or no difference. In this case, it would be that the mean IQ scores for the two populations are equal. The alternative hypothesis is what we are testing against the null hypothesis. Here, it would be that the mean IQ score for subjects with medium lead levels is higher than that for subjects with high lead levels.
Step 3 ：Therefore, the null and alternative hypotheses should be: \(H_{0}: \mu_{1}=\mu_{2}\) and \(H_{1}: \mu_{1}>\mu_{2}\)
Step 4 ：The test statistic is not provided in the question, so we cannot calculate it. However, it would typically be calculated using the sample means, sample standard deviations, and sample sizes of the two populations.
Step 5 ：Final Answer: The null and alternative hypotheses are: \(\boxed{H_{0}: \mu_{1}=\mu_{2}}\) and \(\boxed{H_{1}: \mu_{1}>\mu_{2}}\)
