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Suppose you have a coin and you want to test two hypotheses: H0: the coin is fair (that is, you get a head with probability p = 0.5 and a tail with the same) and H1: the coin is unfair and has probability p > 05 for a head and (1-p) for a tail. Assume p is known.
Explain in detail what the optimum Neyman=Pearson test is for all values of the false alarm probability a in the open interval (0,1).
Be careful of randomization.
When sampling is done for the proportion of defective items in a large shipment, where the population proportion is 0.18 and the sample size is 200, what is the probability that the sample proportion will be at least 0.20?
To test whether the significant difference between two sample variance using F-tests.
History suggests that the average number of hurricanes formed during a year is 6.0 hurricanes. Find the probability of at most three hurricanes being formed during a randomly selected year.
What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 57.3 and 77.7 inches? Please show work.
A point estimate for a parameter is a single number designed to estimate a quantitative parameter of a population, usually the value of the corresponding sample statistic
Assume the data have bell shaped distribution with a mean of 30 and a standard deviation of 5. Employ the empirical rule to determine the percentage of data within each of the following ranges: 20 to 40, 15 to 45, and 25 to 35.
A sample of 148 of our statistics students rated their level of admiration for Hilary Rodham Clinton on a scale of 1 to 7. The mean rating was 4.06 and the standard deviation was 1.70.
Regression and Correlation are two of the most often used and abused tools in research. People are quick to jump to conclusions that if a relationship exists between two variables, then one must cause (causation) the other.
Comment on their success or failure to meet this goal.
The test statistic for a two-sided significance test for a population mean is z = -2.12. What is the corresponding P -value?
Determine the likelihood of accepting a lot which is 1% defective?
Show some work for each part. A diagram can be helpful. A survey of adults found the following: 65 percent of the adults drink coffee. 35 percent drink tea. 80 percent drink coffee or tea (or both). If we choose a surveyed adult at random, find t..
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