question archive A college prep school advertises that their students are more prepared to succeed in college than other schools
A college prep school advertises that their students are more prepared to succeed in college than other schools
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A college prep school advertises that their students are more prepared to succeed in college than other schools. To verify this, they categorize GPA’s into 4 groups and look up the proportion of students at a state college in each category. They find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in GPA. They then take a random sample of 150 of their graduates at the state college and find that 5 has a 0-0.99, 18 have a 1-1.99, 67 have a 2-2.99, and 60 have a 3-4.00. Can they conclude that the grades of their graduates are distributed differently than the general population at the school? Test at the 0.05 level of significance.
Hypotheses:
H0: There is a differenceno difference between the general population and the college prep students in GPA.
H1: There is a differenceno difference between the general population and the college prep students in GPA.
Enter the test statistic - round to 4 decimal places.
Enter the p-value - round to 4 decimal places.
Can it be concluded that there is a statistically significant difference between the general population and the college prep students in GPA?
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Answer:
The statistical software output for this problem is:
Hence,
Ho: There is no difference between the general population and the college prep students in GPA.
H1: There is a difference between the general population and the college prep students in GPA.
Test statistic = 12.1210
p - Value = 0.0070
Conclusion: Yes
PFA
