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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%?
In the year 2000, the state of Indiana began a $40-million renovation of its state fairgrounds, which included the building of a miniature golf course and a state-of-the-art livestock building.
Based on testing, company makes following statement: "Our batteries last the average of 430 to 470 minutes, and our confidence in that interval is 95%" Find out standard deviation and show work.
Based on these results, a confidence interval for the population mean is found to be u = 5.7 PLUS OR MINUS 4.4. Find the degree of confidence.
Create the 99% confidence interval on difference of average ages for viewers of the two TV programs. How can you interpret interval?
Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
The average price for a new home in a certain neighborhood is $275,000 with a standard deviation of $20,000. What is the probability that a particular home will cost between $280,000 and $300,000?
A certain brand of automobile tire has a mean span of 3500 miles and a standard deviation of 2000 miles. (assume the life spans of the tires have a bell-shaped distribution)
A human society claims that less than 36% of US. households own a dog. In random sample of 397 U. S. households, 151 say they own a dog. At mean=0.03, is there enough evidence to support the society's claim?
Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in downtown Toledo, Ohio. They are considering jointly offering child care for their employees.
Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence level for the true mean number of available hotel rooms, based on the point estimate of each sampl..
If absolute value of test statistic is less than critical value in hypothesis test decision is to?
If I have 3 tables in the classroom with 16 girls and 8 boys in the class, what are the chances of 8 girls sitting at one table when seats are assigned randomly?
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