Module 8: Inference for One Proportion
Hypothesis Testing (2 of 5)
Hypothesis Testing (2 of 5)
Learning OUTCOMES
- Recognize the logic behind a hypothesis test and how it relates to the P-value.
In this section, our focus is hypothesis testing, which is part of inference. On the previous page, we practiced stating null and alternative hypotheses from a research question. Forming the hypotheses is the first step in a hypothesis test. Here are the general steps in the process of hypothesis testing. We will see that hypothesis testing is related to the thinking we did in Linking Probability to Statistical Inference.
Step 1: Determine the hypotheses.
The hypotheses come from the research question.
Step 2: Collect the data.
Ideally, we select a random sample from the population. The data comes from this sample. We calculate a statistic (a mean or a proportion) to summarize the data.
Step 3: Assess the evidence.
Assume that the null hypothesis is true. Could the data come from the population described by the null hypothesis? Use simulation or a mathematical model to examine the results from random samples selected from the population described by the null hypothesis. Figure out if results similar to the data are likely or unlikely. Note that the wording “likely or unlikely” implies that this step requires some kind of probability calculation.
Step 4: State a conclusion.
We use what we find in the previous step to make a decision. This step requires us to think in the following way. Remember that we assume that the null hypothesis is true. Then one of two outcomes can occur:
- One possibility is that results similar to the actual sample are extremely unlikely. This means that the data do not fit in with results from random samples selected from the population described by the null hypothesis. In this case, it is unlikely that the data came from this population, so we view this as strong evidence against the null hypothesis. We reject the null hypothesis in favor of the alternative hypothesis.
- The other possibility is that results similar to the actual sample are fairly likely (not unusual). This means that the data fit in with typical results from random samples selected from the population described by the null hypothesis. In this case, we do not have evidence against the null hypothesis, so we cannot reject it in favor of the alternative hypothesis.
Example
Data Use on Smart Phones
According to an article by Andrew Berg (“Report: Teens Texting More, Using More Data,” Wireless Week, October 15, 2010), Nielsen Company analyzed cell phone usage for different age groups using cell phone bills and surveys. Nielsen found significant growth in data usage, particularly among teens, stating that “94 percent of teen subscribers self-identify as advanced data users, turning to their cellphones for messaging, Internet, multimedia, gaming, and other activities like downloads.” The study found that the mean cell phone data usage was 62 MB among teens ages 13 to 1