Statistics and Probability

• Hypothesis- an assumption or conjecture about a population parameter that may or may not be true.
• Null hypothesis (H0)- the statement of no difference between two groups, which is tested against the alternative hypothesis
• Alternative hypothesis (Ha)- the opposite to the null hypothesis, stating there is a significant difference between two groups
• Level of significance- the probability of making a type 1 error
• Null: equal to, the same as, not changed from, is
• Alternative: Not equal, different from, changed from, not the same as.
• $\mu_1 \neq \mu_2$: Alternative
• $\mu_1 =$$\mu_2$: Null
• Alternative: greater than, higher than, longer than, bigger than, increased, at least$>$
• Alternative: less than, lower than, shorter than, smaller than, decreased, fewer than${}$
• Alternative: above, over, beyond, exceeding, surpassed${}>a$
• Alternative: between or among, within, more than one, several, multiple${}\in\left[a, b\right]$
• Alternative: between or among$(a, b)$
• The average age of bus drivers in Metro Manila is 38.8 years. $H sub O: u =$$38.8 years$$H sub a: u is not equal ti 38.8 years$
• Two-tailed: nondirectional
• not equal: two-tailed
• <,>: one-tailed
• Directional test: left or right
• right: >
• left: <
• Always look for the alternative hypothesis
• If p value is greater than alpha (0.05), fail to reject H0
• If p value is less than alpha (0.05), reject H0
• The null hypothesis is always that there is no difference between groups.
• The null hypothesis states that there is no difference between two groups.
• A one-tailed test has only one direction, while a two-tailed test can go either way.
• A directional test is used when we have an idea about which group will be higher/lower.
• The alternative hypothesis states that there is a significant difference between two groups.
• A one-tailed test has only one tail, while a two-tailed test has both tails.
• Type 1: regret-true
• Type 2: accepted-false
• Level of Significance: denoted as $a$
• Level of significance: 1%, 5%, or 10%
• Level of significance: reject or fail to reject (tinanggap mo)
• Type 1 Error: 1% or less- life and death situations
• 5% or 10%- social research
• Critical region: should be rejected
• Non-critical region: should be accepted