Hypothesis testing

Hypothesis testing was the idea of Ronald Fisher, Jerzy Neyman, Karl Pearson and his son, Egon Pearson. It involves making an assumption about a parameter and then testing it to aid in statistical decision making. The assumption is known as a hypothesis. There are two types of hypothesis; null hypothesis and alternate hypothesis

Null hypothesis (denoted by H 0) Alternate hypothesis (denoted by H1 or Ha)
It is a statistical assumption stating that the observations are made by mere chance and there is no difference in the sample mean values It is a contrast of the null hypothesis, stating that observations are due to a certain effect.

Other basic terminologies in hypothesis testing

  1. Level of significance
  2. Going through the assigned case severally will help you to identify the underlying issues. Make short notes on anything you deem crucial while underlining the key points. Also, ensure that you have not missed any key points that strengthen your case.

  3. Type I error (denoted by α)
  4. The error that occurs when one rejects a true null hypothesis. The alpha region showing this critical region can be illustrated with the aid of a normal curve

  5. Type II error (denoted by β)
  6. It occurs when one fails to reject a false null hypothesis. The beta region showing the acceptance region can also be illustrated using a normal curve. The probability of not conducting a type II error is called the power of a test

  7. One-tailed test
  8. Test entailing a statistical hypothesis with one value e.g. H0: µ1= µ2

  9. Two tailed test
  10. A test whose statistical hypothesis assumes the greater than or less than value e.g. H0: µ1≤ µ2

Decision rules in hypothesis testing

A decision in test of hypothesis can be to either reject or not reject the null hypothesis. The P-value and region of acceptance help to determine which decision to make

  1. P-value
  2. it helps to measure the strength of evidence supporting the null hypothesis. If the P-value is less than the significance level, reject the null hypothesis, otherwise, accept it.

  3. Region of acceptance
  4. it contains a range of values and if the test statistic falls within the acceptance region, do not reject the null hypothesis

  5. Example of hypothesis testing (one-sample z-test)
  6. Students in a certain class are believed to possess an above average intelligence. A sample of 30 students is tested with mean score of 112.5. Can we support this claim if the mean population IQ is 100 and the standard deviation is 15?

    Solution:

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