11E Preview

In the next in-class activity, you will need to be able to identify statistical significance and practical significance and describe the factors that affect the size of the P-value.

As you have seen in previous activities, a one-sample test of proportions tests a claim about a single population proportion, and we have learned to use P-values as evidence to support a claim. This preview assignment will discuss the limitations of the P-value and lead to a discussion of hypothesis test errors in the next activity.

Question 1

Suppose you are studying the proportion of people with lower back pain. In a certain  population, 25% of people experience lower back pain. A researcher wants to see if  teaching patients how to stretch and exercise will lower incidences of lower back  pain.

She randomly selects 100,000 people from this population to participate in a study.  She teaches the study participants how to stretch and exercise. After two months,  she evaluates the participants and finds that 24.75% of the participants experience  lower back pain.

  1. Use the DCMP Inference for a Population Proportion tool at  https://dcmathpathways.shinyapps.io/Inference_prop/ to calculate the P value for the test.
  2. At the 5% significance level, do you reject the null hypothesis? Explain.
  3. What is the conclusion, in context?

If a hypothesis test results in rejecting the null hypothesis because the P-value is less  than the significance level, we say we have statistical significance. This means there  is enough evidence against the null hypothesis to convince us to reject the null  hypothesis.

Question 2

In Question 1, did you show “statistical significance?” Explain.

Statistical significance does not necessarily mean the result is interesting or important. If the results are meaningful, we say that the results have practical significance. Having practical significance usually means the results show a significant improvement!

Question 3

In Question 1, did you think you showed “practical significance?” Explain.

Question 4

Suppose another researcher simultaneously conducted a study, but their study only  included 1,200 participants (still a really large study). Similarly, they found that  24.75% of participants experienced back pain.

  1. Use the DCMP Inference for a Population Proportion tool at  https://dcmathpathways.shinyapps.io/Inference_prop/ to calculate the P value for the test.
  2. At the 5% significance level, do you reject the null hypothesis? Explain.
  3. What is the conclusion, in context?
  4. In this study, did you show “statistical significance?” Explain.

 

Question 5

Summarize the values from the study in Questions 1 and 4 in the following table:

Sample Size Sample Proportion P-value
Question 1
Question 4

Question 6

The sample proportions from both studies are exactly the same, but you came to a  different conclusion. What factors contribute to the discrepancy?