1. For each of the scenario’s below write a conclusion to the test that includes
ID: 3131928 • Letter: 1
Question
1. For each of the scenario’s below write a conclusion to the test that includes: the type of test being conducted (one-sample, independent, paired), a decision about the null, the statistics you used to make that decision, and a statement about the results of the test in terms of the variables (what did the researchers find?).
a) Researchers wanted to determine if polar bear health has declined in recent years. The researchers measured a random group of polar bears in 2010 for their overall health (scale of 0-100 with 100 being the best health), then tracked down the same bears using id markers and measured their health using the same metric in 2015. Conducting their analysis researchers calculated a t-statistic of 2.01 (31 degrees of freedom).
b) Researchers wanted to determine if freshman GPAs differ between students from the 1970s and current students. The researchers took a random group of students from the 1970s and calculated their GPA average, then took a random sample of current freshman and calculated their GPA. Conducting their analysis researchers calculated a t-statistic of -1.73 (525 degrees of freedom).
Explanation / Answer
a)
This is a PAIRED T TEST,as the same bears are tested after 5 years.
As t = 2.01, df = 31, then the P value is [as this is one tailed)
P = 0.026601089
As P < 0.05, then we reject Ho. [DECISION]
Hence, there is significant evidence that overall mean bear health in 2010 was greater than overall mean bear health in 2015 at 0.05 level. [CONCLUSION]
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b)
As these are 2 separate groups of samples, then this is AN INDEPENDENT SAMPLES T TEST.
As t = -1.73, df = 525, as this is a two tailed test ["differ" was used], then
P = 0.084217971
As P > 0.05, we FAIL TO REJECT H0. [DECISION]
There is no significant evidence that the true mean GPA of students from 1970s are different from the true mean GPA of the current freshmen at 0.05 level. [CONCLUSION]
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