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Let X1, ..., Xn be a random sample from a normal distribution, Xi ~ N(mu, 1). Find a uniformly most powerful test of Ho: mu = mu(not) against Ha: mu > mu(not).
Derive the generalized likelihood ratio test of Ho: theta = theta(not) against Ha: theta not equal to theta(not). Determine an approximate critical value for size alpha using the large-sample chi-sq
Respective exponential distributions, Xi ~ EXP(theta 1) and Yj ~ EXP(theta 2). Derive the generalized likelihood ratio test of Ho: theta 1 = theta 2 versus Ha: theta 1 not equal to theta 2.
The goal of this project is to to research independent variables of hockey players in the NHL. Display the model for the first multiple regression equation.
The components in subsystem 1 are all of the same design and each has a 1/10,000 chance of failure. The parallel components each has a 3/10,000 chance for failure. What is the overall reliability of
A population has a mean of u =80 and a standard deviation o=16. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64
A system has three states, i.e. good (State 1), degraded (State 2) and failed (State 3). What are the states that need to be considered for a reliability analysis of the system?
How closely related is the new client base to sales performance? Draw the scatterplot and compute the correlation and describe the relationship
The 10 differences (Variety A - Variety B) give the following statistics: x = 0.46 and s = 0.92. Is there convincing evidence that Variety A has the higher mean yield? Carry out a complete significa
The state agriculture department asked random samples of Indiana farmers in each county whether they favored. Find the proportions of farmers in favor of the program in each of the two counties.
Make a plot of the data (this could be a histogram, stemplot, boxplot, or normal probability plot). Be sure to describe what the plot looks like. Are the t procedures justified? Explain.
Do these data give good reason to believe that the mean rent of all advertised apartments is greater than $500 per month? Carry out a complete significance test.
Estimate the mean response to 1 ng of this substance, and give the margin of error for your choice of confidence level. Then explain to a chemist who knows no statistics what your margin of error me
Find the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign.
What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.
If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.
What is the probability of getting a score of 91 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.
Perform an approximate alpha = .10 level test of Ho: mu1 = mu2 against Ha: mu1 not = to mu2 using the equation T = [Y(bar) - X(bar) - (mu2 - mu1)] / sqrt[S1^2/n1 + S2^2/n2] ~ t(v)
Suppose that the number of defects in a piece of wire of length t yards is Poisson distributed, X ~ POI(lambda *t). What is the p-value for such a test?
Suppose that a coin is biased, and the probability of a heads is one of the three values p = .2, .3, or .8. What is the probability of type I error, P[TI]?
Assuming it is known that s^2 = 4, test Ho: mu > or equal to 12 versus Ha: mu < 12 at the significance level alpha = .01. What sample size is needed for the power of the test to be .9 for the al
Compute a 90% confidence interval for the difference between the probability that the Yankees win at home and the probability that they win when on the road.
To help identify these lurking variables, let's discuss the following about experiments related to child-rearing techniques and the nature vs. nuture debate. Why are behavioral studies like this so
Think of a situation in where you work. What are some of the reasons that experiments in the workplace may be difficult to conduct?
The researchers believe that 60% of the snail population has shells that are streaked. Based on the recorded sample of snails, do you find a significant difference from the hypothesized proportion o