Question

Listed below are the lead concentrations in μ​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 17 μ​g/g. Assume that the lead concentrations in traditional medicines are normally distributed. 21.5, 10.5, 12.5,  15, 22, 7.5, 8, 3,14.5, 9

What are the null and alternative​ hypotheses?

test statistic

pval

ending statement

Answer 1

From Sample data ,

= 12.35

S = 6.0830

H0: >= 17

Ha: < 17

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 12.35 - 17 ) / ( 6.083 / √(10) )
t = -2.42

Decision based on P value
P - value = P ( t > 2.4173 ) = 0.0194 (From T table)

Since p-value < 0.05 level reject H0.

We conclude that we have sufficient evidence evidence to support the claim that the mean lead

concentration for all such medicines is less than 17 μ​g/g.