Finals

• Parameter 


  A measure computed on the basis of data obtained from an entire population.
• Statistic 


  A measure computed on the basis of data obtained from a sample.
• Population Proportion


  $P=$$A/N$
• Sampling distribution


  The probability distribution that would be obtained if all possible samples of a particular sample size were taken from the population of the given statistic.
• Standard error


  the standard deviation of the sampling distribution of any statistic.
• $T=$$N^n$(Sampling w/ replacement


  N = population size

  n = sample size
• Sampling w/o replacement 


  $T=$$N!/(n!(N-n)!)$
• Central Limit Theorem


  states that if the population distribution is not necessarily normal, but

  has mean μ and standard deviation σ, then, for sufficiently large n, the

  sampling distribution of the mean is approximately normal.
• The larger the sample size, the closer a distribution is to being normal.
• The rule of thumb is cut-off point is n≥30.
• The difference of two sample proportion is equal to the difference of two population proportion.
• The difference between two sample proportions is approximately normal.
• The sampling distribution of sample proportion is the same as population proportion.
• The sampling distribution of sample proportion is approximately normally distributed if the population is large.
• Estimation 


  the computation of statistic from sample data which yield a value that is an approximation of an unknown true parameter value.
• Estimates


  values of the estimator
• Types of Estimator

  • Point estimator
  • Interval estimator
• Point estimator


  refers to single value of the estimate of the unknown parameter
• PE provides only a single numerical value and is seldom used in problem involving statistical inference.
• Interval Estimator


  range of numerical values w/n which true parameter value to fall w/n is expected to find.
• Confidence Interval


  interval estimate is presented w/ the associate level of confidence
• Degree of confidence - denoted by (1-α)100%
• Decreasing α implies increasing coefficient of confidence.
• Characteristics of a Good Estimator

  • Unbiased
  • Precise
  • Consistent
• Df - degrees of freedom
• Properties of t distribution

  1. Has a mean of 0 and variances greater than 1, but this variance approaches to 1 as the sample size gets larger.
  2. Like the normal distribution is symmetrical about the mean.
  3. The t value ranges from -∞ 𝑡𝑜 + ∞.
  4. The t distribution approaches the normal distribution for large sample sizes.
  5. The t distribution is less peaked in the center and has higher tails as compared to the normal distribution.
• Statistical Inference


  process of drawing conclusions about the population on the basis of the samples obtained from the population of interest.
• Hypothesis testing follows systematic procedures which include:

  • Statistical hypothesis
  • Level of significance
  • Test statistic
  • Critical and acceptance regions
  • Computation of the test statistic
  • Statistical decision
  • interpretation
  • Drawing Conclusion
• The SD of the sampling distribution of mean w/o replacement is not equal to the population mean divided by the square root of the sample size.
• The sampling distribution of mean is the same as the population mean.
• The sampling distribution of mean is approximately normally distributed if the population is large.
• Sample mean differences can be lower or higher than the population mean difference.
• Sign test 


  Non-parametric alternative to one sample t-test
• Sign test

  • used to make inferences about a population median w/o the assumption of normality.
  • variable is on ordinal scale, continuous, and observations are independent
• Sign test


  $S=$$P(K≤k | n, 0.050)$
• Mann-Whitney Test


  non-parametric alternative to the t-test of 2 independent samples
• Mann-Whitney Test

  • requires the assumption of any continuous, ordinal level of measurement of the data
• Mann-Whitney test


  Ties w/n groups have no effect on the test statistic, but those across groups do
• Wilcoxon Signed-rank Test


  non-parametric alternative to the t-statistic of dependent samples
• Wilcoxon Signed-Rank test

  • requires the assumption of any continuous and at least an ordinal level of measurement scale