SOPHIA STATISTICS UNIT 4 MILESTONE FINAL
PAPER 2026 QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
◉ What test would you use if you have data for letter grades and
want to see if it differs from some stated distribution of grades?
Answer: We would have data for one qualitative variable (letter
grade) that has 5 categories (A, B, C, D, F) so we would use the Chi-
Square Goodness-of-Fit Test with df = 5 - 1 = 4
◉ What value of the chi-square statistic do we expect to see if the
null hypothesis is true? Answer: If the null hypothesis is true, then
all of the observed values would be close to the expected values and
we would get a value of chi-square near 0.
◉ What is the form of the null hypothesis for a Chi-Square
Goodness-of-Fit Test? Answer: H₀: Data are consistent with a
specified distribution of percentages in categories
◉ What does the p-value represent in a hypothesis test using the
chi-square distribution? Answer: it is always the area in the right tail
to the right of the chi-square test statistic
, ◉ What hypothesis test would you use if you want to test for an
association between the time of day you take a class (morning,
afternoon, evening) and letter grade? Answer: You would have data
for two qualitative variables (time of day and letter grade) so you
would use the Chi-Square Independence Test
◉ What is P(A and B) if A and B are independent events? Answer:
P(A and B) = P(A) times P(B)
◉ What is the form of the null hypothesis for a chi-square
independence test? Answer: H₀: The variables __ and ___ are
independent
(or there is no association between ___ and __)
◉ What are the two reasons the observed matrix of values and the
expected matrix of values are different in a Chi-square
Independence Test? Answer: 1. The null hypothesis is correct and
the differences are just random sample fluctuations.
2. The null hypothesis is incorrect and we are seeing evidence of
this.
◉ If data were collected for gender and letter grades in stats and you
did a Chi-Square Independence Test and got a p-value of 0.234, what
would the conclusion be? Answer: There is not significant evidence
of an association between gender and letter grades for ALL stat
students.
PAPER 2026 QUESTIONS WITH COMPLETE
SOLUTIONS GRADED A+
◉ What test would you use if you have data for letter grades and
want to see if it differs from some stated distribution of grades?
Answer: We would have data for one qualitative variable (letter
grade) that has 5 categories (A, B, C, D, F) so we would use the Chi-
Square Goodness-of-Fit Test with df = 5 - 1 = 4
◉ What value of the chi-square statistic do we expect to see if the
null hypothesis is true? Answer: If the null hypothesis is true, then
all of the observed values would be close to the expected values and
we would get a value of chi-square near 0.
◉ What is the form of the null hypothesis for a Chi-Square
Goodness-of-Fit Test? Answer: H₀: Data are consistent with a
specified distribution of percentages in categories
◉ What does the p-value represent in a hypothesis test using the
chi-square distribution? Answer: it is always the area in the right tail
to the right of the chi-square test statistic
, ◉ What hypothesis test would you use if you want to test for an
association between the time of day you take a class (morning,
afternoon, evening) and letter grade? Answer: You would have data
for two qualitative variables (time of day and letter grade) so you
would use the Chi-Square Independence Test
◉ What is P(A and B) if A and B are independent events? Answer:
P(A and B) = P(A) times P(B)
◉ What is the form of the null hypothesis for a chi-square
independence test? Answer: H₀: The variables __ and ___ are
independent
(or there is no association between ___ and __)
◉ What are the two reasons the observed matrix of values and the
expected matrix of values are different in a Chi-square
Independence Test? Answer: 1. The null hypothesis is correct and
the differences are just random sample fluctuations.
2. The null hypothesis is incorrect and we are seeing evidence of
this.
◉ If data were collected for gender and letter grades in stats and you
did a Chi-Square Independence Test and got a p-value of 0.234, what
would the conclusion be? Answer: There is not significant evidence
of an association between gender and letter grades for ALL stat
students.
