Hypothesis Testing: Making Inferences from a Sample
Scenario: Imagine that the drug for severe depression from this week’s Discussion was approved for use in humans. Researchers now want to know whether people using this drug have a different life expectancy than the rest of the general population. A sample of 100 patients who use the drug are followed over time. Those that use the drug have a mean life expectancy of 71.30 years. The mean life expectancy for the general population is 75.62 years. The population standard deviation is 28.
Identify the independent and dependent variables.
Independent Variable:
An independent variable is the variable that we have control over and we can manipulate (Welkowitz, Cohen, & Lea, 2012). In this case, the independent variable is the drug. The drug can be manipulated to be either the medication or a placebo.
Dependent Variable:
The dependent variable is the variable that we measure and what is affected during the course of our experiment (Welkowitz et al., 2012). The life expectancy is what we are measuring and it is what is affected because of using the drug.
Explain whether the researcher should use a one-tailed or a two-tailed z test and why.
Two tailed tests are the norm (Welkowitz et al., 2012). Researchers should use a two-tailed test to see if the two means are different from each other. Researchers want to know if those using the drug have a different life expectancy. This could go either way. In a one tailed test, a researcher would only be interested in an alternate hypothesis that states H₁: μ > μ₀ or H₁: μ < μ₀, but not both.
Null Hypothesis
The null hypothesis would state that the drug does not have an effect on the life expectancy of the user.
Alternate Hypothesis
The null hypothesis would state that the drug does have an effect on the life expectancy of the user.
Calculate the obtained z score by hand and state the critical value with an alpha of .05
**Z-score:
$z = \ \frac{71.30 - 75.62}{\sqrt{100}} = \ \frac{- 4.32}{10} = \ - 0.432$
Critical value:
$1 - 0.05 = 0.95$
$\frac{0.95}{2} = 0.475$
$1.9 + 0.06 = \mp 1.96$
Would you retain or reject the null hypothesis? Why?
Our null hypothesis is retained because the z-score of -0.432 is in between our critical value of 1.96 and -1.96.
Explain whether the results are significant, and why or why not.
The results are non-significant because the obtained value did not fall beyond the critical value.
What should the researcher conclude about the life expectancy of the sample in comparison to the population?
The researcher should conclude that there is no difference between the life expectancy of the sample and the general population.
Explain the relationship between z scores and the standard deviation
A z-score will tell you how far away the mean and a particular value is in terms of standard deviation.