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 H0) 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

  • Level of significance

It refers to the degree of significance which allows the researcher to reject or not reject the null hypothesis. A significance level of 5% is usually used since the results cannot be 100% accurate

  • Type I error (denoted by α)

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

  • Type II error (denoted by β)

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

  • One-tailed test

Test entailing a statistical hypothesis with one value e.g. H0: µ1= µ2

  • Two tailed test

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

P-value: 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.

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

Example of Hypothesis Testing (one-sample z-test)

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

Since the population mean is 100, null hypothesis H0: µ=100

Alternate hypothesis H1: µ>100

From the z-table, the z-score of an area of 0.05= 1.645

Test statistic, x-µ0δ/⎷n= (112.5-100)/ (15/ 30) = 4.56

The test statistic does not lie within the region of acceptance. Since the test statistic is greater than the tabulated z-score, reject the null hypothesis.

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