This question: 1 point(s) possible Submit quiz Listed below are the lead concentrations in $\mu g / g$ measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than $13 \mu \mathrm{g} / \mathrm{g}$. Assume that the sample is a simple random sample. \[ \begin{array}{lllllllllll} 11.5 & 22 & 4.5 & 21 & 17 & 7.5 & 4 & 7.5 & 6 & 8.5 & 0 \end{array} \] Assuming all conditions tor conducting a nypothesis test are met, what are the null and alternative nypotheses? A. $H_{0}: \mu=13 \mu g / g$ \[ \mathrm{H}_{1}: \mu>13 \mu \mathrm{g} / \mathrm{g} \] C. \[ \begin{array}{l} H_{0}: \mu>13 \mu g / g \\ H_{1}: \mu<13 \mu g / g \end{array} \] B. \[ \begin{array}{l} H_{0}: \mu=13 \mu g / g \\ H_{1}: \mu<13 \mu g / g \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu=13 \mu g / g \\ H_{1}: \mu \neq 13 \mu g / g \end{array} \] Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed) Next

Step 1 ：Given the lead concentrations in traditional medicines, we are asked to test the claim that the mean lead concentration for all such medicines is less than $13 \mu g / g$ at a 0.10 significance level.

Step 2 ：The null and alternative hypotheses for this test are: \n $H_{0}: \mu=13 \mu g / g$ \n $H_{1}: \mu<13 \mu g / g$

Step 3 ：We calculate the sample mean, standard deviation, and size from the given data.

Step 4 ：The sample mean is $9.95 \mu g / g$, the sample standard deviation is $7.16 \mu g / g$, and the sample size is 11.

Step 5 ：We then calculate the test statistic using the formula: \n $t = \frac{\bar{x} - \mu_{0}}{s / \sqrt{n}}$

Step 6 ：Substituting the values, we get the test statistic as $-1.41$.

Step 7 ：We also calculate the degrees of freedom as $n - 1 = 10$.

Step 8 ：Using the test statistic and degrees of freedom, we calculate the P-value for a one-tailed test.

Step 9 ：The P-value is $0.094$.

Step 10 ：Final Answer: \n The null and alternative hypotheses are: \n $H_{0}: \mu=13 \mu g / g$ \n $H_{1}: \mu<13 \mu g / g$ \n The test statistic is \(\boxed{-1.41}\). \n The P-value is \(\boxed{0.094}\).