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A pharmaceutical company manufactures large batches of analgesic caplets which are designated to contain 200 mg of aspirin. The concentration of aspirin per caplet is actually a random variable X normally distributed about a mean 200 mg with standard deviation known to be 7.5 mg when the manufacturing process is in "control". As a Quality Control exercise small random samples of n caplets are taken from each production run and tested for potency.
A random sample of n = 16 caplets is selected with a view to testing the hypotheses: H0: m = 200 mg H1: m ≠ 200 mg
Assuming a type I error of 5%, determine the critical region(s) for this test in terms of the sample mean.
What is the probability of a type II error for this test if the true mean is in fact 195 mg?
What impact would reducing the sample size have on the type I and type II errors?
The observed mean for the sample of 16 observations was found to be 203 mg. Calculate the "p-value" associated with this sample statistic. Based on the stated hypotheses, what do you conclude? Would your conclusion change if a = 10%?
Assuming a significance level of 5% is to be used, what size sample should be taken if it is required that we reject H0 if the true mean deviates from 200 mg by 5 mg or more with power of at least 90%?
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The Niko electronics company just manufactured 5000 CDs, and 3% are defective. If 10 of these CDs are randomly selectedd for testing, what is the proability tha the entire batch is will be rejected.
A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test would return unacceptable type II errors. Which od the following would solve this problem.
Doctors nationally believe that 68% of a certain type of operation are successful. In a particular hospital 47 of these operations were observed and 37 of them were successful. At a = 0.05 is this hospital's success rate different from the nationa..
As long as there is either an upward or downward trend in the data, will a k-period moving average have a smaller mean square error than a moving average obtained with k+1 periods? Why or why not?
Our decisions depend on how the options are presented to us. Here's an experiment that illustrates this phenomenon. Tell 20 subjects that they have been given $50 but can't keep it all.
Would you conclude that your data set is approximately normal? If so, what percentage of your data values lie:
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