pter 21 ou overheard your professors mention that seniors at SVU were better pre
ID: 3321369 • Letter: P
Question
pter 21 ou overheard your professors mention that seniors at SVU were better prepared for college when they were freshmen compared to the current freshmen. You decided to see if your professors were right by comparing high school GPAs of seniors and freshmen at SVU (after all, high school GPA is supposed to produce success in college, right?). So, you collect data from 100 freshmen (sample 1) and 90 seniors (sample 2). After plugging all of the data into Excel, you come up with the following: Freshmen - average HS GPA 3.57, s 0.45 Seniors-average HS GPA = 3.67, s = 0.28 Please provide the following answers: a. df? b. Critical t-value c. Calculated t-value d. Interpret the findings -first, using a rough p-value and a statement regarding significance, then in non-stats languageExplanation / Answer
Standard error. Compute the standard error (SE) of the sampling distribution.
SE = sqrt[ (s12/n1) + (s22/n2) ]
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
putting the values
sqrt[ (0.45^2/100) + (0.28^2/90) ] = 0.053
Degrees of freedom. The degrees of freedom (DF) is:
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
If DF does not compute to an integer, round it off to the nearest whole number. Some texts suggest that the degrees of freedom can be approximated by the smaller of n1 - 1 and n2 - 1; but the above formula gives better results.
DF = (0.45^2/100 + 0.28^2/90)^2 / { [ (0.45^2 / 100)^2 / (100 - 1) ] + [ (0.28^2 / 90)^2 / (90 - 1) ] } = 167.92 ~ 168
Test statistic. The test statistic is a t statistic (t) defined by the following equation.
t = [ (x1 - x2) - d ] / SE
(3.57-3.67)/0.053
where x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
t = -1.8867
we find the p value for given t score , alpha = 0.05 qnd 2 tail test
The P-Value is .061021.
The result is not significant at p < .05.
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