Question

Give an example from a future Health Profession of a mean or a proportion for which you would like to do a Hypothesis Test. As shown in the text your Null and Alternative hypothesis MUST include the symbol for a Population parameter along with your hypothesized claimed numerical value for this parameter. Then discuss the ramifications of making a Type I Error and a Type II Error in the context of your stated Null and Alternative Hypotheses.

Answer 1

Let us consider an example from the future health profession for testing of hypothesis. Suppose, the researcher wants to check whether the average body mass index of the teenagers is increased due to modern life facilities. It was revealed from previous studies that the average body mass index for teenagers in the USA was 21.5. The population standard deviation is given as σ = 5.3. For this scenario, we need to conduct the one sample z test for the population mean. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The average body mass index of the teenagers in the USA is 21.5.

Alternative hypothesis: H_a: The average body mass index of the teenagers in the USA is greater than 21.5.

H₀: µ = 21.5 versus H_a: µ > 21.5

This is a one tailed test. (Upper tailed/Right tailed)

We know that the type I error is the probability of rejecting the null hypothesis when it is true. The type I error in context of above test is given as the probability of rejecting the null hypothesis that the average body mass index of the teenagers in the USA is 21.5, however actually average body mass index is 21.5.

The type II error is the probability of do not rejecting the null hypothesis when it is not true. The type II error in context of above test is given as the probability of do not rejecting the null hypothesis that the average body mass of the teenagers in the USA is 21.5, however actually average body mass index is greater than 21.5.