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Listed below are the lead concentrations in ug/g measured in different traditional medicines. Use a 0.05...

Listed below are the lead concentrations in ug/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 14 ug/g.

​17.5         3.5            12.5         9                4                9.5            20.5         10             10.5         21

Solutions

Expert Solution

Values ( X ) Σ ( Xi- X̅ )2
17.5 32.49
3.5 68.89
12.5 0.49
9 7.84
4 60.84
9.5 5.29
20.5 75.69
10 3.24
10.5 1.69
21 84.64
Total 118 341.1

Mean X̅ = Σ Xi / n
X̅ = 118 / 10 = 11.8
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 341.1 / 10 -1 ) = 6.1563

To Test :-

H0 :- µ = 14
H1 :- µ < 14

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 11.8 - 14 ) / ( 6.1563 / √(10) )
t = -1.1301


Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
t(α, n-1) = t(0.05 , 10-1) = 1.833
t > -t(α, n-1) = -1.1301 > - 1.833
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.1301 ) = 0.1438
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.1438 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the mean lead concentration for all such medicines is less than 14 ug/g.


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