Stats

• mean, proportion, variance and standard deviation may becomputed using sample data or population data
• Measures computed using sample data are called statistics
• measures computed using population data are called parameters
• Suppose that under the same condition, several samples (S1, S2, S3,…)are taken from the population. Thus, the sample mean (𝑥1, 𝑥2, 𝑥3, … )may be considered a random variable.Probability distribution of statistics and other measurements ofsamples are called sampling distribution.
• The mean of the sample means will be the sameas the population mean
• Standard Deviation of the sampling distribution of ҧ 𝑥 (also known as the standard error) is calculated using either of the two formulas
• The sample size is considered small compared to the population size if the sample size is equal to or less than 5% of the population
• As the sample size n increases without limit, the shape of thedistribution of the sample means taken with replacement from apopulation with mean 𝜇 and standard deviation 𝜎 will approacha normal distribution
• 𝑧 = x-u/oUsed when the data are directlylifted from the population𝑧 = x-u/o/nUsed when the data are takenfrom the sample
• When the original variable is normally distributed, the distribution ofthe sample means will be normally distributed, for any sample size n. When the distribution of the original variable might not be normal, asample size of 30 or more is needed to use a normal distribution toapproximate the distribution of the sample means. The larger thesample, the better the approximation will be.
• hypothesis - which is a decision-making process for evaluating claims about a population
• hypothesis - basically a testing of assumption you can make on a population
• hypothesis - an assumption or conjecture on a population parameters which may or may not be true
• statistical hypothesis is a conjecture about a population parameter.this conjecture may or may not be true
• null hypothesis - symbolized by h0. it is the initial claim. there is no significant difference, no changes, nothing happened, and no relationship between two parameters
• null hypothesis - there is no significant difference between a parameter and a specific value, or between two parameters
• alternative hypothesis - symbolized by ha. it is contrary to the claim. there is a significant difference, an effect, change, and a relationship between two parameters.
• alternative hypothesis - there is a significant difference between a parameter and a specific value, or between two parameters
• the null hypothesis is generally a statement of no change. Thus, a statement of equality ( = ) or one which involves equality is usually considered in the null hypothesis ( ≥ or ≤ )
• The statistical hypothesis is about a parameter or distribution of thepopulation values.
• The null and alternative hypotheses are complementary and must not overlap
• The rejection of the nullhypothesis Ho leads to theacceptance of thealternative hypothesis Ha
• A directional alternative hypothesis is an assertion that one measure isgreater than another measure. It involves quantifiers < or >
• < is lower tail while > is upper tail
• A non-directional alternative hypothesis is a statement that asserts thatone value is different from another. It involves the quantifier ≠
• A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected or accepted
• A one-tailed test is used to test a null hypothesis against a directional alternative hypothesis
• A two-tailed test is used to test a null hypothesis against a non-directional alternative hypothesis
• The numerical value obtained from a statistical test is called the test value or test statistic.
• A correct decision was made when a true null hypothesis is notrejected or when a false null hypothesis is rejected.A Type I error is committed when a true null hypothesis is rejectedA Type II error is committed when a false null hypothesis is notrejected.
• z test – used when the population mean and standard deviationare known, and the sample size is large (n ≥ 30)
• t test – used when the population standard deviation is unknownand must be estimated from the sample data, and the samplesize is small (n < 30)
• A test statistic is a numerical value computed from the sample data.
• STATISTICAL TESTS FORRELATIONSHIPPearson Product Moment CorrelationCoefficient (or Pearson r)Spearman Rank Order Correlation(or Spearman ρ)Chi square test of Independence(or x2 test)STATISTICAL TESTS FOR DIFFERENCEz-Test for Independent ProportionIndependent t-TestDependent t-Test (or Paired t-Test)One-way Analysis of Variance(One-Way ANOVA
• The z test is a statistical test for the mean of a population
• z-test - It can be used when n ≥ 30 or when the population is normallydistributed and 𝜎 is known
• right tailed test

  computed is greater than critical = reject
• left tailed test

  computed is lesser than critical = reject
• two tailed

  computed is greater than critical = reject
• null: claim

  reject h0

  the claim is invalid