Define each of the following terms: sampled population, random sampling, convenient sampling, judgmental sampling, stratified random sampling, consistency in sampling, relative efficiency. Explain why a sample is of probabilistic nature.
What is it meant by the term “parameter of a population”? Explain why a population can be represented by a random variable.
What is a point estimate, and an unbiased point estimate? Explain how the sample mean can be an unbiased estimate of the population mean. How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.
Please define each of the following terms, discuss applicability and significance of each: sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity.
What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions? What are the limitations of the central limit theorem, and how some of these limitations are bypassed? For example, the z statistic as the sampling distribution in estimating a proportion.
What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?
What is the alternative of the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How is this sampling distribution constructed as a combination of a z distribution and a chi squared distribution? What are the properties of this distribution?
Please define each of the following terms and provide hypothetical example for each: hypothesis testing, null and alternative hypothesis, non-directional and directional hypothesis, type I error in testing hypothesis, type II error in testing hypothesis, probability of type I error (ɑ), probability of type II error (ß), power of the test and its significance, the critical value(s) in a test, p value (significance level).
What is the difference between testing hypothesis on a population and testing hypothesis when comparing two populations? Provide hypothetical examples.
What are the possible outcomes in testing a hypothesis? What are the determinant factors in deciding the critical value(s) in testing a hypothesis?
When the z statistic is appropriate to be used in testing a hypothesis? When the t statistic is appropriate to be used in testing a hypothesis? For each case, include the underlying assumptions, and the test statistic, for both testing a hypothesis on the mean of population, and testing hypothesis in comparing the value of the mean in a population with the value of the mean in another population. What is the criterion for rejecting the null hypothesis for both non-directional and directional tests? How do you find the p value in each case? Do not forget to discuss cases that involve proportion(s).
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