Question

isted below are the lead concentrations in muμ​g/g measured in different traditional medicines. Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 13 muμ​g/g. 5.5 5 8 19 6.5 12.5 9 3 10.5 3

Answer 1

= (5.5 + 5 + 8 + 19 + 6.5 + 12.5 + 9 + 3 + 10.5 + 3)/10 = 8.2

s = sqrt(((5.5 - 8.2)^2 + (5 - 8.2)^2 + (8 - 8.2)^2 + (19 - 8.2)^2 + (6.5 - 8.2)^2 + (12.5 - 8.2)^2 + (9 - 8.2)^2 + (3 - 8.2)^2 + (10.5 - 8.2)^2 + (3 - 8.2)^2)/9) = 4.8944

H₀: = 13

H₁: < 13

The test statistic t = ()/(s/)

                            = (8.2 - 13)/(4.8944/)

                           = -3.101

At alpha = 0.05, the critical value is t^* = -1.833

Since the test statistic value is less than the critical value(-3.101 < -1.833), so we should reject the null hypothesis.

There is sufficient evidence to support the claim that the mean lead concentration for all such medicines is less than 13 mug/g.