Listed below are the lead concentrations in ug/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

18ug/g.

22.5

9

18.5

22

16

18.5

15

3

8

6

This question is incomplete, the complete question is;

Listed below are the lead concentrations in ug/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  18ug/g.

22.5 , 9 , 18.5 , 22 , 16 , 18.5 , 15 , 3 , 8, 6

a) what is the null and alternative hypothesis

b) determine the test statistic

a)

the null and alternative hypothesis will be;

Null hypothesis            H₀ : Ц = 18 ug/g

Alternative hypothesis  H₁ : Ц < 18 ug/g

b) the Test Statistic = -1.47

Step-by-step explanation:

Given data;

x = 22.5 , 9 , 18.5 , 22 , 16 , 18.5 , 15 , 3 , 8, 6

number of observation n = 10

level of significance ∝ = 0.01

a)

the null and alternative hypothesis will be;

Null hypothesis             H₀ : Ц = 18 ug/g

Alternative hypothesis  H₁ : Ц < 18 ug/g

b)

Test statistics;

using the formula;

t = (x" - Ц) / (s/√n)

x" is the sample mean

s is the standard deviation

Ц is the population mean ( 18 )

n is the number of observation ( 10 )

for first we get our mean x"

mean x" = ∑x / n

mean x" = (22.5  + 9  + 18.5  + 22  + 16  + 18.5  + 15  + 3  + 8 + 6) / 10

mean x" = 138.5 /10

mean x" = 14.85

Next we find the standard deviation s    

standard deviation s = √[ (∑(x-x")²) / (n - 1)]

x                     (x - x")                    (x - x")²

22.5                7.65                       58.5225

9                      -5.85                      34.2225

18.5                  3.65                       13.3225

22                    7.15                         51.1225

16                     1.15                          1.3225

18.5                  3.65                        13.3225

15                    0.15                         0.0225

3                      -11.85                       140.4225

8                     -6.85                        46.9225

6                     -8.85                        78.3225

total                                                437.525

so we substitute to get our standard deviation

standard deviation s = √[ (   437.525 / (10 - 1)]

= √[ 437.525 / 9]

= √48.6138

standard deviation s = 6.9723

Finally our we substitute our values into the Test statistics formula

t = (x" - Ц) / (s/√n)

t =  (14.85 - 18) / (6.9723/√10)

t = -3.25 /  2.2048

t =  -1.47

Therefore the Test Statistic = -1.47