Question

Listed below are the lead concentrations in mu​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 12 mu​g/g. Assume that the lead concentrations in traditional medicines are normally distributed. 8     13.5     2.5     11     6.5     22     4.5     8.5     6.5     8

Answer 1

Solution:

x	x2
8	64
13.5	182.25
2.5	6.25
11	121
6.5	42.25
22	484
4.5	20.25
8.5	72.25
6.5	42.25
8	64
∑x=91	∑x2=1098.5

Mean ˉx=∑xn

=8+13.5+2.5+11+6.5+22+4.5+8.5+6.5+/10

=91/10

=9.1

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√1098.5-(91)210/9

=√1098.5-828.1/9

=√270.49

=√30.0444

=5.4813

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 12

Ha : < 12

Test statistic = t

= ( - ) / S / n

= (9.1-12) / 5.48 / 10

= -1.673

Test statistic = t = -1.673

P-value =0.0643

= 0.01  

P-value >

0.0643 > 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that