P-value hypothesis testing

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  1. Introduction to P-value
  1. Proportion Hypothesis Testing
    From a sample of 100 university students, it was found that 58 of them have taken a mathematics course throughout their university career. Test the claim that "Most university students have taken a math course". Do this using the P-Value method with a significance level of α=0.05\alpha=0.05.
    1. Cole and Thomas throw a house party and offer free beer to people who come dressed up in Christmas theme. Thomas makes the claim "75% of people who come to our party will dress up". By the end of the night 102 people dressed up, and 48 people didn't dress up. Using the P-Value method with a 95% confidence level is Thomas' claim true?
      1. 120 cars were sampled and it was found that the average size of fuel tanks were 46L. The standard deviation of the size of fuel tanks for all cars is 5L. Test the claim that "the average size of a gas tank for a car is 45L" using the P-Value method with a significance level of α=0.01\alpha=0.01
        Topic Notes
        Instead of using the Standard Normal Distribution to find the Z-score relating to the significance level, all you need to do is put the Test-Statistic on the Standard Normal Distribution and see if the "smaller" area (called the P-Value) is less than the given significance level (α\alpha).

        \cdot P-Value \leq α\alpha \Rightarrow H0H_0 is false
        \cdot P-Value > α\alpha \Rightarrow Fail to reject H0H_0