Question

Hypothesis Testing

you must discuss the topic, how it relates to every day life and something you learned about the topic

Answer 1

• A hypothesis testevaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.

  The purpose of hypothesis testing is to make a decision in the face of uncertainty. We do not have a fool-proof method for doing this: Errors can be made. Specifically, two kinds of errors can be made: Type I Error: We decide to reject the null hypothesis when it is true.

• Hypothesis Testing
  
  Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps.
  
  1. Formulate the null hypothesis (commonly, that the observations are the result of pure chance) and the alternative hypothesis (commonly, that the observations show a real effect combined with a component of chance variation).
  
  2. Identify a test statistic that can be used to assess the truth of the null hypothesis.
  
  3. Compute the P-value, which is the probability that a test statistic at least as significant as the one observed would be obtained assuming that the null hypothesis were true. The smaller the -value, the stronger the evidence against the null hypothesis.
  
  4. Compare the -value to an acceptable significance value (sometimes called an alpha value). If , that the observed effect is statistically significant, the null hypothesis is ruled out, and the alternative hypothesis is valid.

• example of hypothesis testing example 1 :

  The school principal wants to test if it is true what teachers say – that high school juniors use the computer an average 3.2 hours a day. What are our null and alternative hypotheses?

  h0 : µ = 3.2 Ha : µ1\neq 3.2 Our null hypothesis states that the population has a mean equal to 3.2 hours. Our alternative hypothesis states that the population has a mean that differs from 3.2 hours.

  example 2:

  We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. What are our null and alternative hypotheses?

  H0 : µ = 14 Ha : µ1\neq14 Our null hypothesis states that the population has a mean equal to 14 milligrams. Our alternative hypothesis states that the population has a mean that is different than 14 milligrams.