Question

4 Listed below are the lead concentrations in yolg measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicinos is less than 14 gg. Assume that the sample is a simple random sample. 13 165 5.5 10.5 15.5 125 9 175 30 Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? OA. Ho: > 14 wg/ OB. H: 14 polg H, με 14 μας He: #14919 Oc. Họ k = 14 ugg OD. H: 14919 H, με 14 μας Hy: > 14 910 Determine the test statistic (Round to two decimal places as needed.)

Answer 1

Solution:

x	x2
13	169
16.5	272.25
5.5	30.25
10.5	110.25
4	16
15.5	240.25
12.5	156.25
9	81
17.5	306.25
3	9
∑x=107	∑x2=1390.5

Mean ˉx=∑xn

=13+16.5+5.5+10.5+4+15.5+12.5+9+17.5+3/10

=107/10

=10.7

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

=√1390.5-(107)210/9

=√1390.5-1144.9/9

=√245.6/9

=√27.288/9

=5.22

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 14

H_a : $\mu$ < 14

Test statistic = t

= (
T
- $\mu$ ) / S / $\sqrt$ n

= (10.7-14) / 5.22 / $\sqrt$ 10

= −1.999

Test statistic = t =  −1.999

P-value =0.038

$\alpha$ = 0.10

P-value < $\alpha$

0.038< 0.10

Reject the null hypothesis .

There is sufficient evidence to conclude that the mean lead concertation for all such medicnes less than 14