Statistics

• Hypothesis testing

  a process wherein we make decisions in evaluating claims about the population, based on the sample taken form the same population.
• Level of Significance (alpha) - probability that we will reject the null hypothesis when it is actually true
• 6 steps of Hypothesis Testing

  I. State the null and alternative hypotheses.

  II. Select the level of significance.

  III. Select the Statistical Tool (Z-test, T-Test, CLT)

  IV. Formulate the decision rule.

  V. Compute the value of the test statistics.

  VI. Make a Decision.
• Null Hypothesis

  is a statement about the value of a population parameter formulated with the hope of it being rejected. It is usually denoted by Ho.
• If Ho is rejected, we will be led to accept an Alternative Hypothesis, usually denoted by Ha.
• A null hypothesis always involves an equality symbol. ( =, ≥, ≤ )
• An alternative hypothesis contains the inequality symbol. ( >, <, ≠ )
• constant of alpha (ą) = 0.05 or 5%
• Correct Decision

  failed to reject (Ho) and it is true
• Type II Error

  failed to reject (Ho) and it is false
• Type I Error

  rejected (Ho) and it is true
• Correct Decision

  rejected (Ho) and it is false
• Z-Test

  mean known

  population standard deviation known

  normally distributed

  n is greater than or equal to 30

  n≥30
• T-test

  population standard deviation ~ unknown

  n is less than 30

  n < 30
• CLT ( Central Limit Theorem )

  Sample size is sufficiently large, s may be used if a is unknown
• • if the test-statistic value that you computed falls in the rejection region, we need to reject the null hypothesis, and in that process, we accept the alternative hypothesis. In this case, there is enough evidence to reject the null hypothesis.
• if the test-statistic value that you computed falls in the acceptance region, we accept the null hypothesis. The evidence is not enough to reject the null hypothesis
• The alternative nypothesis is...

  one-sided ~ one tailed test

  two - sided ~ two - tailed test

  
• rejection region I critical region

  set of all values of the test statistic that couses us to reject the null nypotheris
• non- rejection region / acceptance region

  set of an volues of the test statistic that causes us to fail to reject the null hypothesis
• If the level of significance ( alpha ) is 0.05 or 5%, what is the left and right tailed of one-tailed?

  Left - tailed = -1.645

  Right - tailed = 1.645
• If the level of significance ( alpha ) is 0.01 or 1%, what is the left and right tailed of one-tailed?

  Left - tailed = -2.33

  Right - tailed = 2.33
• If the level of significance ( alpha ) is 0.001 or 0.01%, what is the left and right tailed of one-tailed?

  Left - tailed = -3.09

  Right - tailed = 3.09
• If the level of significance is 0.05 the two-tailed is +/- 1.96
• If the level of significance is 0.01 the two-tailed is +/- 2.58
• If the level of significance is 0.001 the two-tailed is +/- 3.30
• Correlation analysis is used to determine and describe the relationship between two variables.
• Univariate data is only one variable and measures by a central tendency
• Bivariate data

  two variables
• Scatter plot

  graph of two variables in a rectangular coordinate plane displaying a relationship between the two variables
• Input variable (x)

  ~ independent variable

  ~ controlled variable

  ~ cannot be affected by other variable
• Output variable (y)

  ~ dependent variable

  ~ results from the controlled variable

  ~ affected by changes in the IV
• Trend

  determines the direction of the points
• linear ~ trend of straight line

  non-linear ~ trend of curve line
• Pearson’s sample correlation coefficient (also known

  as Pearson r ), denoted by r, is a test statistic that measures thestrength of the linear relationship between two variables.
• correlation coefficient (r) is a number between -1 and 1

  that describes both the strength and the direction of correlation.
• Correlation Analysis

  in symbol, we write 1 ≤ r ≤ 1