yr1 chap 7 hypothesis testing

• the null hypothesis is represented by $H_0$

  the alternative hypothesis is represnted by $H_1$
• the null hypothesis is what is assumed to be true
• the alternative hypothesis is what would be true if the assumption is incorrect
• a test statistic is the result of the experiment that you are testing
• the critical region is the set of values of the test statistic which would lead to the null hypothesis being rejected
• if the alternative hypothesis is in the form p < ... or p > ... then you carry out a one-tailed test
• if the alternative hypothesis is in the form p != ... then you carry out a two-tailed test
• the actual significance level of a test is different to the significance level given in the question, it is the probability that X is within the critical region
• to carry out a one-tailed hypothesis test:

  • write out the null hypothesis and alternative hypothesis
  • let X = whatever the test statistic should be
  • write out the model in the form X ~ B(n, p)
  • write the probability you need to test, rearrange until it is in the form P(X less than or equal to x)
  • find the probability, write it down
  • compare the probability to the significance level
  • if the probability is larger, accept the null hypothesis
  • if the probability is smaller, reject the null hypothesis
  • add context, there is/is not sufficient evidence to...
• to carry out a two-tailed hypothesis test:

  • write out the null hypothesis and alternative hypothesis
  • let X = whatever the test statistic should be
  • write out the model in the form X ~ B(n, p)
  • write the probability you need to test, rearrange until it is in the form P(X less than or equal to x)
  • find the probability, write it down
  • compare the probability to half of the significance level
  • if the probability is larger, accept the null hypothesis
  • if the probability is smaller, reject the null hypothesis
  • add context, there is/is not sufficient evidence to...