Stats and Prob 2

• Null Hypothesis (Ho)


  Original hypothesis
• Alternative Hypothesis (Ha)


  Opposite of the original hypothesis
• One-tailed test

  Rejects the null hypothesis if the test statistic is in the rejection region on one side of the distribution
• Two-tailed test


  Rejects the null hypothesis if the test statistic is in the rejection regions on both sides of the distribution
• Mean (M)


  Average value
• Sample mean (X)


  Average value of the sample
• Standard deviation (σ)


  Measure of the spread of a distribution
• Sample size (n)


  Number of observations in the sample
• Hypothesis testing


  1. State null and alternative hypothesis

  2. Calculate test statistic

  3. Compare test statistic to critical value

  4. Determine if null hypothesis is rejected or not
• Hypothesis testing example 1

  • Null hypothesis: Machine dispenses 50ml of fluid on average

  Alternative hypothesis: Machine does not dispense 50ml of fluid on average

  Test statistic: Z = (75 - 50) / (2.5/√40) = -5.06

  Reject null hypothesis at 95% confidence level
• Hypothesis testing example 2

  • Null hypothesis: Battery lifespan is 2 years or more

  Alternative hypothesis: Battery lifespan is less than 2 years

  Test statistic: T = (1.8 - 2) / (0.15/√10) = -4.22

  Reject null hypothesis at 99% confidence level
• Hypothesis testing with proportions example

  • Null hypothesis: Proportion of residents owning a cellphone is 70%

  Alternative hypothesis: Proportion of residents owning a cellphone is not 70%

  Test statistic: Z = (0.65 - 0.70) / √((0.70)(0.30)/200) = -1.54

  Fail to reject null hypothesis at 90% confidence level
• Hypothesis testing with proportions example 2


  • Null hypothesis: Proportion of residents owning a vehicle is 60% or less

  Alternative hypothesis: Proportion of residents owning a vehicle is more than 60%

  Test statistic: Z = (0.68 - 0.60) / √((0.60)(0.40)/250) = 2.55

  Reject null hypothesis at 90% confidence level
• Type I error


  Rejecting the null hypothesis when it is true
• Type II error


  Failing to reject the null hypothesis when it is false
• Type I error has greater consequence than Type II error