PLEASE HELP e samples 200 random York students and either has them drink either
ID: 3325277 • Letter: P
Question
PLEASE HELPe samples 200 random York students and either has them drink either no coffee, or 2 cups of coffee every day for a whole semester the end of the semester, she found that in the Coffee group, 79 out of 100 passed all their he hired you as a statistical consultant. Represent the data in a well-crafted figure. Analyze these data and draw the most reasonable conclusion(s) hat scientific question(s) are you trying to answer? 0 courses, and in the No Coffee group, 68 out of 100 passed all their courses List your null hypotheses and altermate hypotheses, if any. o Propose two changes to the experiment that would reduce bias, sampling error, or artifacts
Explanation / Answer
Answer :
Here we want to compare customer response in two different cases (with coffee and without coffee) in this problem and we want to evaluate whther the proportion is effectively constant . This means statistically we want to compare two or more binomial populations have same parameter p i.e whther p1 = p2=p.
So hre Scientificaly we want to test whether taking 2 cups of coffee everyday has an impact on passing the exam.
We will use Chi-Square test to test this hypothesis . As for large samples sampling distribution is approximately Normal (Z= (Xi -ni pi)/(Sqrt(ni pi (1-ni pi))) whre ni is sample size pi is prob of success for ith population.
and square of this follows Chi square distribution.
Null Hypothesis Ho: pass proportion of coofee group = pass proportion of non-coffee group
Alternate Hypothesis Ha : pass proportion of coofee group <> pass proportion of non-coffee group
Assumng level of significance = 0.05
Test Statistic Chisquurae = 2 = sum of Squrar(Obj -expected )/expected .
Based on the same Results of Test of Hypothesis for given data is as follows
Coffee
Noncoffe
passed
79
68
147
failed
21
32
53
Total
100
100
200
Criterion
chi SQ0.05 at 1 degrees of Freedom : 3.841
Reject Null Hypothesis if Chisquare calculated > 3.841
Coffee
Noncoffe
passed-observed
79
68
Passed -Expected
73.5
73.5
Obs -expected
5.5
-5.5
Sqr(Obs -expected)
30.25
30.25
Sqr(Obs -expected)/expected
0.411565
0.411565
Chi Square : sum of Sqr(Obs -expected)/expected
0.823129252
Hence Chi Square calculated is < 3.841 , Null Hypotheis cannot be rejected , which indicates There is no significant difference observed in passing proportion between coffeee and noncoffee groups.
Additional changes to improve accurace , instead of pass fail actual marks can be checked for variability.
Check feasibility of removing subject factor by evaluating impact on few more subjects with varied level of difficulty
Coffee
Noncoffe
passed
79
68
147
failed
21
32
53
Total
100
100
200
Criterion
chi SQ0.05 at 1 degrees of Freedom : 3.841
Reject Null Hypothesis if Chisquare calculated > 3.841
Coffee
Noncoffe
passed-observed
79
68
Passed -Expected
73.5
73.5
Obs -expected
5.5
-5.5
Sqr(Obs -expected)
30.25
30.25
Sqr(Obs -expected)/expected
0.411565
0.411565
Chi Square : sum of Sqr(Obs -expected)/expected
0.823129252
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