Question

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 16 μ​g/g.

21     

33     

6.5     

20.5     

9.5     

13.5     

16.5     

15.5     

13.5     

99

What are the null and alternative​ hypotheses?

Determine the test statistic

State the final conclusion that addresses the original claim.

(Reject or Fail to Reject) H0. There is (not sufficient or sufficient) evidence to conclude that the mean lead concentration for all such medicines is (greater than or not or equal to or less than) 16 μ​g/g.

Answer 1

Step 1:

Ho: ≥ 16

Ha: < 16 (Claim)

Step 2: Test statistics

n = 10

sample mean = 248.50 / 10 = 24.85

sample sd = s

data	data-mean	(data - mean)2
21.00	-3.85	14.8225
33.00	8.15	66.4225
6.50	-18.35	336.7225
20.50	-4.35	18.9225
9.50	-15.35	235.6225
13.50	-11.35	128.8225
16.50	-8.35	69.7225
15.50	-9.35	87.4225
13.50	-11.35	128.8225
99.00	74.15	5498.2225

Assuming that the data is normally distributed and also as the population sd is not given, we will use t stat.

Step 3:

df = 9

= 0.01

The t-critical value for a left-tailed test, for a significance level of α=0.01

tc = −2.821

As t stat (1.035) does not fall in the rejection region, we fail to reject the Null hypothesis.

Fail to Reject H0. There is not sufficient evidence to conclude that the mean lead concentration for all such medicines is less than16 μ​g/g.