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When we test a simple null hypothesis against a composite alternative, a critical region is said to be unbiased if the corresponding power function takes on its minimum value at the value of the parameter assumed under the null hypothesis. In other words, a critical region is unbiased if the probability of rejecting the null hypothesis is least when the null hypothesis is true. Given a single observation of the random variable X having the density
where -1 θ 1, show that the critical region x α provides an unbiased critical region of size α for testing the null hypothesis θ = 0 against the alternative hypothesis θ 0.
An educational study utilizes a simple pre post design to assess the efficacy of a computer tutor for solving inequalities.
27% fall into both categories. What is the probability a randomly selected student commutes and does not participate in a student organization?
Suggest one psychological research question that could be answered by each of the following types of statistical tests:
A real estate builder wishes to determine how house size (house) is influenced by family income (income), family size (Size) and education of the head of household (School).
We want to know if his support has decreased. In computing a test of hypothesis with , what is the estimate of the overall proportion?
Use alpha level. 05 to compute and interpret Pearson's r and to test whether it is important (using all your steps for hypothesis test).
The Starbucks in the Bauer College of Business found that 24% of customers purchase more than one cup of coffee per day from their shop. If 180 customers are randomly selected one day, what is the probability that no less than 25% of them purchase..
A binary mobile consists of two branches, a left branch and a right branch. Each branch is a rod of a certain length, from which hangs either a weight or another binary mobile. We can represent a binary mobile using compound data by constructing i..
A sample of 30 students are tested (sample mean=58, standard error=3.2). Compute a 99 percent confidence interval based on this sample's data. How do these students compare to the national sample?
What are the three criticisms of null hypothesis statistical testing?
stock repurchasesbeta industries has net income of 1700000 and it has 1830000 shares of common stock outstanding. the
Construct a 98% con?dence interval for the mean change in heart rate. Assume that the population has a normal distribution. Interpret your answer.
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