Question

Listed below are the lead concentrations in ?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 1 5 ?g/g. 11 12 3 3.5 10 6 15.5 20.5 19 15.5 Determine the test statistic. (Round to two decimal places as needed.) State the final conclusion that addresses the original claim Click to select your answer(s)

Answer 1

To test $H_0:\mu = 15$ against $H_1:\mu < 15$

Here

sample mean $\bar{x} = 11.6$

sample standard deviation

and sample size

The test statistic can be written as

$t = \frac{\sqrt{n}(\bar{x}-15)}{s}$ which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 10% level of significance if $t_{obs}<-t_{0.05,n-1}$

Now,

The value of the test statistic

and critical value

Since $t_{obs} = -1.75395 \nless t_{0.05,9} = -1.83311$ , we fail to reject H₀ at 10% level of significance and we can conclude that the mean lead concentration of all such medicines is less than 15 $\mu g/g$