Question 1193308: Exergaming in Canada. Exergames are active video games such as rhythmic dancing games, virtual bicycles, balance board simulators, and virtual sports simulators that require a screen and a console. A study of exergaming practiced by students from grades 10 and 11 in Montreal, Canada, examined many factors related to participation in exergaming.23 Of the 358 students who reported that they stressed about their health, 29.9% said that they were exergamers. 23 Of the 851 students who reported that they did not stress about their health, 20.8% said that they were exergamers.
A)Define the two populations to be compared for this exercise.
B)What are the counts, the sample sizes, and the proportions?
C)Are the guidelines for the use of the large-sample confidence interval satisfied?
D)Are the guidelines for the use of the large-sample significance test satisfied?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **A. Populations**
* **Population 1:** Students in grades 10 and 11 in Montreal, Canada, who stress about their health.
* **Population 2:** Students in grades 10 and 11 in Montreal, Canada, who do not stress about their health.
**B. Counts, Sample Sizes, and Proportions**
* **Population 1 (Stressed about health):**
* Sample size (n1): 358 students
* Number of exergamers (x1): 0.299 * 358 ≈ 107 students
* Proportion of exergamers (p1): 0.299
* **Population 2 (Not stressed about health):**
* Sample size (n2): 851 students
* Number of exergamers (x2): 0.208 * 851 ≈ 177 students
* Proportion of exergamers (p2): 0.208
**C. Guidelines for Large-Sample Confidence Interval**
Guidelines for using the large-sample confidence interval for the difference in proportions typically include:
* **n1 * p1 ≥ 10**
* **n1 * (1 - p1) ≥ 10**
* **n2 * p2 ≥ 10**
* **n2 * (1 - p2) ≥ 10**
Let's check:
* 358 * 0.299 = 107.02 ≥ 10
* 358 * (1 - 0.299) = 250.98 ≥ 10
* 851 * 0.208 = 177.008 ≥ 10
* 851 * (1 - 0.208) = 673.992 ≥ 10
**All conditions are met, so the guidelines for using the large-sample confidence interval are satisfied.**
**D. Guidelines for Large-Sample Significance Test**
The guidelines for using the large-sample significance test are generally the same as for the confidence interval:
* **n1 * p1 ≥ 10**
* **n1 * (1 - p1) ≥ 10**
* **n2 * p2 ≥ 10**
* **n2 * (1 - p2) ≥ 10**
**Since these conditions were already verified in part C, the guidelines for using the large-sample significance test are also satisfied.**
**Note:** These guidelines are generally considered sufficient for most practical purposes.
Let me know if you have any other questions or would like to proceed with the analysis!
|
|
|
