Application: Hypothesis Testing: Making Inferences from a Sample

Hypothesis testing is the foundation of conducting research in psychology. Researchers must first determine the question they wish to answer and then state their prediction in terms of null and alternative hypotheses. Once the hypotheses are stated, researchers move on to data collection. However, once the results come in, the real challenge is to determine if they have meaning; that is, are the results statistically significant?

For example, a researcher asks whether the drug for severe depression from this week's Discussion leads to a different life expectancy than the general population of people with severe depression. After stating the hypotheses and collecting data, the researcher sees that the mean life expectancy for the people taking the drug is not exactly the same as the rest of the population, but is the difference meaningful (that is, statistically significant) or just due to random variation? There must be a statistically significant difference in order to say that the null hypothesis should be rejected and the people taking the drug really do have a different life expectancy than the population.

Scenario:

A researcher asks if eighth-grade students attending a private middle school have higher or lower scores on a test of reading comprehension when compared to the population of eighth-graders attending publicly-funded schools. A sample of 144 private school eighth-graders take the same exam that all public school 8th graders take at the end of the school year. The private school students have a mean test score of 220.8 and the mean score for the public school students is 204.2, with a standard deviation of 11.4.
Assignment:

To complete this Assignment, submit by Day 7 responses to the following:

• State the independent and dependent variables and explain how you know which is which.

• Explain whether the researcher should use a one-tailed or a two-tailed z test and explain why.

• State the null hypothesis in words (not formulas).

• State the alternative hypothesis in words (not formulas).

• Calculate the obtained z score by hand. Provide your calculations in your Assignment submission (i.e., show your work).

• When alpha is set at .05, the critical value is ± 1.96. Would you retain or reject the null hypothesis? Explain why?

• Are the results significant? How do you know?

• What should the researcher conclude about the reading comprehension of the private school students in comparison to the population?

• In general, explain the relationship between z scores and the standard deviation.

Be sure to justify your responses with evidence from the text and learning resources.