A pharmaceutical manufacturer is concerned that the impurity

A pharmaceutical manufacturer is concerned that the impurity concentration in pills exceeds 3%. It is known from a particular production run, impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. This hypothesis test has already been run.  

What type of test statistic was used and for how many samples?

What type of test was this? (upper tail, lower tail or two tailed)

Test the hypotheses suggested in the problem. Show all steps and state the appropriate managerial conclusion.

Impurity Concentration

Null Hypothesis                    m=

0.0300

Level of Significance

0.0500

Population Standard Deviation

0.0040

Sample Size

64

Sample Mean

0.0307

Standard Error of the Mean

0.0005

Test Statistic

1.4000

One Tail Critical Value

1.6449

One tail p-Value

0.0808

Two Tail Critical Value

1.9600

Two tail p-Value

0.1615

Solution

What type of test statistic was used and for how many samples?

Z test

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What type of test was this? (upper tail, lower tail or two tailed)

upper tail

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Test the hypotheses suggested in the problem. Show all steps and state the appropriate managerial conclusion.

Ho: mu=0.03 (i.e. null hypothesis)

Ha: mu >0.03 (i.e. alternative hypothesis)

The test statistic is

Z=1.4

The p-value= 0.0808

Since the p-value is larger than 0.05, we do not reject Ho.

So we can not conclude that the impurity concentration in pills exceeds 3%