Question

Listed below are the lead concentrations in u​g/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 18 u​g/g.

7     22     19.5     15     7     4.5     15.5     22.5     4.5     19.5

What are the null and alternative​ hypotheses?

A.)H0​: u=18μ​g/g H1​: u>18μ​g/g .

B.) H0​: μequals=18 μ​g/g H1​: μ≠18 μ​g/g

C.) H0​:μ>18 μ​g/g H1​: μ<18 μ​g/g

D.)H0​: μ=18 μ​g/g H1​: μ<18 μ​g/g

2)Determine the test statistic. nothing ?(Round to two decimal places as? needed.)

3)Determine the? P-value. nothing ?(Round to three decimal places as? needed)

4)State the final conclusion that addresses the original claim.

Fail to reject/Reject H0. There is sufficient/not sufficient evidence to conclude that the mean lead concentration for all such medicines is less than/equal to/greater than not 18 ug/g.

Answer 1

Solution :

Listed below are the lead concentrations in u​g/g measured in different traditional medicines. We have to use a 0.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 18 u​g/g.

(1) To determine the appropriate Null and Alternative Hypothesis :

(2) To find the test statistic :

From the data given , we have the following information :

Thus , the value of the test statistic is given as ,

(3) To find the p - value of the test :

To conclude from the test hypothesis test using \alpha = 0.05 level of significance :

(4) Decision :   

(4) Conclusion : Clearly, the p - value of the above t - test is greater than the level of significance (), thus, we FAIL TO REJECT the Null Hypothesis H₀ at 0.01 level of significance and conclude on the basis of the given data that there is NO SUFFICIENT EVIDENCE that the mean lead concentration for all such medicines is LESS THAN 18 ug/g ................. Correct Options (Ans)

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