Statistical Inference, Part 5

Question 1: Discuss populations of continuous, discrete and categorical variables, and the distributions that may be associated with each.

Answer 1: Some populations consist of continuous variables and may be associated with normal distribution, uniform continuous distributions, or other continuous distributions. Such populations, even when they are not associated with any distribution or the distribution is unknown, will nearly always have a population mean and variance. Some populations consist of discrete variables and are associated with discrete distributions such as the uniform discrete distribution, the binomial distribution, or the multinomial distribution. Each outcome is identified with a discrete numerical value.Some populations consist of categorical variables and are associated with binomial, multinomial, geometric, negative binomial, or hypergeometric distributions. Variables may be assigned values from sample sets containing two outcomes, such as {success, failure}, {red ball, white ball} or {yes, no} and are associated with a binomial distribution. Variables may be assigned values from sample sets with more than two outcomes, such as {yes for candidate A, yes for candidate B, yes for candidate C} and are associated with a multinomial distribution.

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Question 2: List some population parameters and sample parameters.

Answer 2: Population parameters are characteristics of the population, whereas sample statistics are characteristics of a sample of the population. The following are some characteristics of populations and characteristics of samples of those populations.?Number of elements in a finite population?Number of observations in sample from a finite or infinite population?Number of elements in the ?th finite population?Number of observations in ?th sample from a finite or infinite population?Proportion of outcome ?1 in population. Sample space is {?1, ?2}.??/?, where ? is number of outcome ?1in sample. Sample space is {?1, ?2}.?Proportion of outcome ?1 in ?th population. Sample space is {?1, ?2}.??/?, where ? is number of outcome ?1in sample from ?th population. Sample space is {?1, ?2}.

Question 3: List more population parameters and sample parameters.

Answer 3: Population parameters are characteristics of the population, whereas sample statistics are characteristics of a sample of the population. The following are some characteristics of populations and characteristics of samples of those populations.?,?Proportion of outcome ? in ?th population. Sample space is {?1,..,?..}.?,??,?/?, where ?,? is number of outcome ? in ?th population. Sample space is {?1,..,?..}.?Mean of a finite or infinite population?Estimate of mean calculated from sample of size ?. Subscript often omitted.?Mean of the ?th finite or infinite population?,?Estimate of mean ?th finite or infinite population, calculated from sample of size ?. First subscript often omitted.?2Population variance of X?2Estimate of variance of X calculated from sample of size ?. Subscript often omitted.?2Population variance of ??Standard error of ?, equal to ?(1-?)/??2Population variance of ?(?=?)?Standard error of ?, equal to ?2/?zza4zz

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