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 14 mu​g/g.

17.5, 2.5, 18, 4.5, 4.5, 14, 10.5, 12.5, 5.5, 4.5

What are the null and alternative​ hypotheses?

Determine the test statistic ____ (round to two decimals)

State the final conclusion that addresses the original claim.:

(Fail to reject Reject) ____ H0. There is ____ (not sufficient or sufficient) evidence to conclude that the mean lead concentration for all such medicines is ___14 μ​g/g

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the mean lead concentration for all such medicines is 14 mu​g/g.

Alternative hypothesis: Ha: the mean lead concentration for all such medicines is less than 14 mu​g/g.

H0: µ = 14 versus Ha: µ < 14

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 14

Xbar = 9.4

S = 5.83476173

n = 10

df = n – 1 = 9

α = 0.1

Critical value = -1.3830

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (9.4 - 14)/[ 5.83476173/sqrt(10)]

t = -2.4931

P-value = 0.0171

(by using t-table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean lead concentration for all such medicines is less than 14 mu​g/g.