MATH1280 Statistics 1 Discussion forum UNIT7
Grades 9.75/0-10
Applying what you have learned.... When politicians make claims that we need to spend a large amount of money to achieve a goal, the claim is often made without legitimate evidence to support a claim that a given program will have a particular result. Let's say that a politician wants to implement a nation-wide education program. The politician gave four examples of schools that used the program: scores at the schools increased 0.5, 1, 2, and 2.5 points respectively (the nation-wide average of the scores is 70). The politician gave no additional evidence about the effectiveness of the program.
Your task: What questions or comments would you have pertaining to the statistical claim made by the politician? You might inquire about the sample, the sampling methods, the full population, the sampling distribution of the mean, and whatever would be useful to more accurately or precisely describe the effectiveness of the program. At the end of your post, state whether you would conclude that the program will increase scores nation-wide.
Note that it is a separate question of whether it is "worth it" to effect change by taking money from people in the form of taxes to pay for a program. Other than (optionally) saying that you think the statistics can or can not answer such a question, the "worth it" question is not part of this discussion.
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1. What questions or comments would you have pertaining to the statistical claim made by the politician? You might inquire about the sample, the sampling methods, the full population, the sampling distribution of the mean, and whatever would be useful to more accurately or precisely describe the effectiveness of the program.
・The sample size
Sample size refers to a representative of the real population for that specific study, and we can know a group of subjects that are selected from the general population through this. But as Yakir explains, "samples that are too small may be unreliable, and larger samples, when possible, are better" (2011, p.18). There is no description of the number of participants, so if the number of participants in each sampsmalllittle, we can say the survey's validity is suspicious. I will question the politician to show a sample size.
・The sample method
There is no description of how the sample data was taken. If there is any mechanism for partial extraction, bias can occur, and the sample can be biased. For example, when data is extracted from the people who answered the questionnaire, the target will be biased if only the respondents are analyzed because they have some intention at the time of answering the questionnaire. I will question the politician to explain about sample method.
・The full population
To get the expected result, more citizens need to be involved in the program, and the data obtained needs to match the estimated projections.
・The sampling Distribution
Sampling Distribution identifies "the probability of each value of the sample average, thus obtaining the sampling distribution of the sample average" (Yakir, 2011, p.106). We can know the mean score of each sample, and we can know more detailed trends as a whole. I will ask the politician to show a more detailed sampling distribution.
2. At the end of your post, state whether you would conclude that the program will increase scores nation-wide.
I cannot conclude that this program will increase scores nation-wide with only the information given. More detailed information is required.
Reference
Yakir. B, (2011). Introduction to Statistical Thinking (With R, Without Calculus). Retrieved from https://my.uopeople.edu/pluginfile.php/1097279/mod_book/chapter/267923/MATH1280RInstall Notes. pdf
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