Question

Listed below are lead concentrations (in ug/g) as measured in herbal medicines commonly available over the counter in the US. The FDA lead standard is 14 ug/g for such medicines. Use the P-value method at a 0.05 significance level to test the claim that the mean lead level for all such herbal medicines is less than the FDA standard. 3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5 Address the following questions:

Is this a left tailed, right tailed or two tailed test?

What is alpha?

Are their any conditions that must be met before you can solve this problem?

What is the null and alternative hypothesis and where is the claim?

What formula did you use and what is the test statistic?

What is your decision and what P-Value did you use?

In simple terms, state the final conclusion that addresses the original claim.

Answer 1

Left tailed

alpha = 0.05

• In theory, the data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ).
• The data must be reasonably random.
• The sample must be less than 10% of the population.

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 14
Alternative Hypothesis, Ha: μ < 14

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (11.05 - 14)/(6.4612/sqrt(10))
t = -1.444

P-value Approach
P-value = 0.0913
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the mean lead level for all such herbal medicines is less than the FDA standard