STAT 101 LEC PART II

• What is an example of comparing two populations?

  Average time spent on social media
• What parameters can be estimated in Module 5.1

  Population mean and population proportion
• What are related samples?

  Samples matched by important characteristics
• What are independent samples?

  Unrelated sets of units measured for a variable
• How does the selection of samples affect their classification?

  Selection method determines related or independent status
• Why are the samples in scenario (b) considered related?

  Both scores are from the same students
• What does scenario (c) illustrate about the samples?

  Independent samples from different brands
• How many individuals rated Milk Teh and Milk Koya?

  Thirty individuals
• What is the significance of pairing in related samples?

  Each individual provides two ratings
• How many shuttlecocks were tested in scenario (c)?

  Twenty from each brand
• What is the main focus of the activity at the end of the section?

  Identifying related or independent samples
• What is the parameter of interest when comparing two population means?

  The difference between the two population means
• What is the notation for the difference between two population means?

  µD = µ1 − µ2
• What is the null hypothesis in hypothesis testing?

  Ho: µD = D0
• What assumptions must be satisfied before using parametric tests?

  Interval scale, random sampling, normal distribution
• What are the cases for estimating two population means?

  1. Known population variances
  2. Unknown population variances (equal variances)
  3. Unknown population variances (unequal variances)
• What is the test procedure for unknown population variances with equal variances?

  Pooled t-test
• What is the test procedure for unknown population variances with unequal variances?

  Non-pooled t-test (Welch’s test)
• What is the significance of the test statistic in hypothesis testing?

  It helps determine the significance of µD
• How does the formulation of null and alternative hypotheses differ in one-tailed tests?

  It involves setting specific inequalities
• What is the definition of related samples?

  Samples matched by important characteristics
• What is the definition of independent samples?

  Unrelated sets of units measured for a variable
• Why is it important to distinguish between related and independent samples?

  It affects the choice of statistical methods
• What is the significance of the sampling distribution of $\hat{\mu}_D$?


  It is normal with mean $\mu_D$ and variance
• How does sample size affect hypothesis testing?

  Larger samples reduce variability in estimates
• What is the role of random sampling in statistical methods?

  It ensures unbiased representation of populations
• What is the concept of confidence intervals in estimation?

  Range of values likely to contain the population parameter
• How does variance relate to hypothesis testing?

  It affects the precision of the test statistic
• What does the table summarize regarding interval estimators?

  Different estimators based on population variances
• What is the condition for using a Z-test?

  Population variances are known
• When should a pooled t-test be used?

  When population variances are unknown and equal
• What is the appropriate test when population variances are unequal?

  Non-pooled t-test (Welch’s test)
• What are the steps to formulate null and alternative hypotheses for one-tailed tests?

  • Define the parameter (e.g., µD = µ1 − µ2)
  • Set null hypothesis (e.g., µD = 0)
  • Set alternative hypothesis (e.g., µD > 0 or µD < 0)
• What is the implication of defining the parameter differently in hypothesis testing?

  The results of the test remain the same
• What is the most appropriate test when population variances are known?


  1. Pooled t-test
• What should be done if population variances are unknown?

  Perform a test on equality of variances
• What is the role of indigenous people (IP) in relation to nature?

  Protectors of nature and heritage
• What threats do indigenous people face?

  Poverty, encroachment, and land grabbing
• What is the aim of the Hinereben Foundation?

  Promote the welfare of indigenous people
• Why does the executive director focus on Sitio Magsaysay?

  IP farmers there are more financially in need