Question

Listed below are the lead concentrations in mu​g/g measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 16 mu​g/g. Assume that the lead concentrations in traditional medicines are normally distributed.

11     6.5     10     3.5     21.5     5     22     8     19.5     4  

What are the null and alternative​ hypotheses?

Determine the test statistic.

​(Round to two decimal places as​ needed.)

Determine the​ P-value.

(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

Answer 1

Solution:

x	x2
11	121
6.5	42.25
10	100
3.5	12.25
21.5	462.25
5	25
22	484
8	64
19.5	380.25
4	16
∑x=111	∑x2=1707

Mean ˉx=∑xn

=11+6.5+10+3.5+21.5+5+22+8+19.5+410

=111/10

=11.1

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

=√1707-(111)210/9

=√1707-1232.1/9

=√474.9/9

=√52.7667

=7.2641

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 16

Ha : < 16

Test statistic = t

= ( - ) / S / n

= (11.1-16 ) / 7.26 / 10

= −2.13

Test statistic = t =  −2.13

P-value =0.062

= 0.10

P-value <

0.062 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that