SOLUTION: Hello� I am sorry, but i really need help with this problem. i have no idea of how to do it... Thank you very much. Exercise 1: A pharmaceutical company is concerned that the i

Question 380537: Hello� I am sorry, but i really need help with this problem. i have no idea of how to do it... Thank you very much.
Exercise 1:
A pharmaceutical company is concerned that the impurity concentration in pills does not exceed 2%. It is known that from a particular production run, impurity concentrations follow a normal distribution with standard deviation 0.3%. A random simple of 64 pills from a production run was checked and the sample mean impurity concentration was found to be 2.06%.
a)Test at the 5% level the null hypothesis that the population mean impurity concentration is 3%.
b)Find the probability of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 2.10%.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A pharmaceutical company is concerned that the impurity concentration in pills does not exceed 2%.
It is known that from a particular production run, impurity concentrations follow a normal distribution with standard deviation 0.3%.
A random simple of 64 pills from a production run was checked and the sample mean impurity concentration was found to be 2.06%.
---------------------
a)Test at the 5% level the null hypothesis that the population mean impurity concentration is 3%.
Ho: p = 0.03
Ha: p is not equal to 0.03
-----
Critial Values: z = +-1.96
Test Statistic: z(0.026) = (0.026-0.03)*sqrt[0.03*0.97/64) = -0.1878
Since the test stat is not less than -1.96 (reject interval) fail to
reject Ho.
Conclusion: The test supports the claim that the mean impurity concentration
level is 3% at the 5% significance level.
=================================================
b)Find the probability of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 2.10%.
I'll look at this.
Cheers,
Stan H.
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