stats and proba

• central theorem
• Random sample of size n are drawn from a

  population = n (becomes larger)
• n = increases (spread of the distributions

  decreases)
• n ≥ 30 = normality of the sampling distribution

  of sample mean
• name of symbols

  A) sample mean

  B) population mean

  C) population standard deviation

  D) sample size

  
• basic steps in problem solving Step 1: identify the given

  ➢ Step 2: what is asked

  ➢ Step 3: formula to be used

  ➢ Step 4: solution with final answer
• hypothesis testing
• Supposition or proposed explanation

  ➢ Made on the basis of limited evidence

  ➢ Starting point for further investigation

  ➢ Evaluating claims

  ➢ If one is true, then the other must be false
• 2 TYPES OF HYPOTHESES

  NULL HYPOTHESIS (H0)

  ➢ No difference

  ➢ =, ≤, ≥

  ALTERNATIVE HYPOTHESIS (H1)

  ➢ Difference

  ➢ ≠, >, <
• 1. Null hypothesis = no change (=, ≤, ≥)

  2. Parameter = population values (μ)

  3. Null and alternative hypotheses =

  complementary and must not overlap
• 2 TYPES OF ALTERNATIVE HYPOTHESIS

  NON-DIRECTIONAL (TWO-TAILED TEST)

  ➢ Probability is found on both tails

  ➢ ≠

  ➢ Two-tailed test

  DIRECTIONAL (ONE-TAILED, LEFT TAIL)

  ➢ Probability is found at the left tail

  ➢ > or <

  ➢ Left-Tailed: Decrease, less than, smaller and the

  like

  ➢ Right-tailed: Greater, efficient, improves,

  effective, increases
• REJECTION REGION

  ➢ Also known as critical region

  ➢ Set of all values of the test statistics

  ➢ Causes us to reject the null hypothesis
• THE NON-REJECTION REGION

  ➢ Acceptance region

  ➢ Set of all values of the test statistics

  ➢ Fail to reject the null hypothesis
• THE CRITICAL VALUE

  ➢ Point boundary

  ➢ Test distribution that is compared

  ➢ Determine if the null hypothesis would be

  rejected
• SIGNIFICANCE VALUE

  ➢ Also known as alpha or α

  ➢ Measure of the strength of the evidence in

  sample

  ➢ Effect = statistically significant
• n ≥ = considered sufficiently large

  ➢ se z test = replacing the population standard

  deviation (σ) by sample standard deviation (s)in

  the formula
• ASSUMPTION

  ➢ Assumed to be unknown and n is the t-test for a

  single mean
• T-TEST FORMULA

  ➢ Population variance is assumed to be unknown

  and n
• DEGREE OF FREEDOM

  ➢ Measure of how many values can vary in sample

  statistics