In: Math
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
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.