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List two reasons why the data may differ.
Can you tell if one researcher is correct and the other one is incorrect? Why?
No, we do not have enough information to make such a claim.
Would you expect the data to be identical? Why or why not?
How might the researchers gather random data?
Take a simple random sample from each group. One way is by assigning a number to each patient and using a random number generator to randomly select patients.
Suppose that the first researcher conducted his survey by randomly choosing one state in the nation and then randomly picking 40 patients from that state. What sampling method would that researcher have used?
Suppose that the second researcher conducted his survey by choosing 40 patients he knew. What sampling method would that researcher have used? What concerns would you have about this data set, based upon the data collection method?
This would be convenience sampling and is not random.
Use the following data to answer the next five exercises: Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data.
| Hours Played per Week | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 0–2 | 26 | 0.17 | 0.17 |
| 2–4 | 30 | 0.20 | 0.37 |
| 4–6 | 49 | 0.33 | 0.70 |
| 6–8 | 25 | 0.17 | 0.87 |
| 8–10 | 12 | 0.08 | 0.95 |
| 10–12 | 8 | 0.05 | 1 |
| Hours Played per Week | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 0–2 | 48 | 0.32 | 0.32 |
| 2–4 | 51 | 0.34 | 0.66 |
| 4–6 | 24 | 0.16 | 0.82 |
| 6–8 | 12 | 0.08 | 0.90 |
| 8–10 | 11 | 0.07 | 0.97 |
| 10–12 | 4 | 0.03 | 1 |
Give a reason why the data may differ.
Would the sample size be large enough if the population is the students in the school?
Yes, the sample size of 150 would be large enough to reflect a population of one school.
Would the sample size be large enough if the population is school-aged children and young adults in the United States?
Researcher A concludes that most students play video games between four and six hours each week. Researcher B concludes that most students play video games between two and four hours each week. Who is correct?
Even though the specific data support each researcher’s conclusions, the different results suggest that more data need to be collected before the researchers can reach a conclusion.
As part of a way to reward students for participating in the survey, the researchers gave each student a gift card to a video game store. Would this affect the data if students knew about the award before the study?
Use the following data to answer the next five exercises: A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were asked to use the software program twice a day, once in the morning and once in the evening. The studies observed 200 stroke patients recovering over a period of several weeks. The first study collected the data in [link] . The second study collected the data in [link] .
| Group | Showed improvement | No improvement | Deterioration |
|---|---|---|---|
| Used program | 142 | 43 | 15 |
| Did not use program | 72 | 110 | 18 |
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