STT 231 EXAM 3 QUESTIONS AND
ANSWERS 2026 VERIFIED.
A study was conducted to identify the factors affecting quality of sleep for university students. A
survey of 290 students of different majors aged 17-29 years old revealed that 67.2% of these
students suffered from poor sleep.Further analyses were conducted based off the original study
of 290 university students in the question above. A second study assessed if the distribution of
sleep quality was the same for the various age groups of Young (19 years old or younger),
Middle (over19 but less than 24 years old), and Old (24 years and older) university students. The
following data shows the sleep quality results for each group.a. Select the name of the test that
should be used to assess if the distribution of the responses is the same for the three age-group
populations
𝜒 ^2 test of independence or 𝜒^2 goodness of fit test - ANS 𝜒^2 test of independence
chi squared test of independence - ANS A statistical test in which both variables are
categorical. This test generally tells us if the distribution of participants across categories is
different from what would happen if there were no difference between the groups
Squared test statistic has two consequences - ANS 1. all x^2 statistics are positive
2. cells that are already unusual are further emphasized (side effect)
Chi-square distributions are skewed to the ______ and take on only _______ values. -
ANS Right, positive
What is standard deviation in chi-squared? - ANS sqrt(2df)
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, chi squared goodness of fit - ANS A hypothesis test that assesses whether the distribution of
a single categorical variable follows a proposed distribution.
Using the 𝜒 2 statistic, it compares the observed counts with the counts we would expect to see
if the observed data perfectly obeyed the proposed distribution.
USES A SINGLE CATEGORICAL VARIABLE.
degrees of freedom - ANS k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule) - ANS expected value =
(column total)(row total) / overall total
If the distribution of the sleep quality is the same for the three age populations of university
students, what is the expected value of the test statistic? - ANS 2
If the distribution of sleep quality is the same for the three age populations of university
students, (i.e., if sleep quality is independent of age group) how would you determine the
expected count of young students reporting "good"quality sleep? [Set up the calculation you
would perform using values from the table of results; you do not need to complete the
computation. - ANS (𝟐𝟔 + 𝟒𝟖 + 𝟐𝟏) ∗ 𝟕𝟕/𝟐𝟗𝟎 across the row * total / overall total
The observed 𝜒 " test statistic was computed to be 4.73. The table belowshows the observed
counts for each joint outcome between age group andsleep quality, along with the expected
counts in parentheses. Which cell contributed the largest amount to the overall 𝜒 " = 4.73? The
least? Provide a2-3 sentence justification of your answer. - ANS The cell that contributes the
most is students in the old group reporting good sleep, since the difference between observed
and expected of ~6 is largest relative to the size of the expected count. The group with the
smallest contribution is the young students experiencing bad sleep, because the difference
between observed and expected counts is smallest relative to the expected count size for that
cell. We could also calculate the contributions foreach to verify the response above.
The p-value associated with the overall test statistic of 𝜒 " = 4.73 was 0.09395with estimated
effect size 𝑉7 = 0.1277. Which of the following statement(s)correctly interprets the p-value?
@COPYRIGHT ALL RIGHTS RESERVED PAGE 2 OF 10
ANSWERS 2026 VERIFIED.
A study was conducted to identify the factors affecting quality of sleep for university students. A
survey of 290 students of different majors aged 17-29 years old revealed that 67.2% of these
students suffered from poor sleep.Further analyses were conducted based off the original study
of 290 university students in the question above. A second study assessed if the distribution of
sleep quality was the same for the various age groups of Young (19 years old or younger),
Middle (over19 but less than 24 years old), and Old (24 years and older) university students. The
following data shows the sleep quality results for each group.a. Select the name of the test that
should be used to assess if the distribution of the responses is the same for the three age-group
populations
𝜒 ^2 test of independence or 𝜒^2 goodness of fit test - ANS 𝜒^2 test of independence
chi squared test of independence - ANS A statistical test in which both variables are
categorical. This test generally tells us if the distribution of participants across categories is
different from what would happen if there were no difference between the groups
Squared test statistic has two consequences - ANS 1. all x^2 statistics are positive
2. cells that are already unusual are further emphasized (side effect)
Chi-square distributions are skewed to the ______ and take on only _______ values. -
ANS Right, positive
What is standard deviation in chi-squared? - ANS sqrt(2df)
@COPYRIGHT ALL RIGHTS RESERVED PAGE 1 OF 10
, chi squared goodness of fit - ANS A hypothesis test that assesses whether the distribution of
a single categorical variable follows a proposed distribution.
Using the 𝜒 2 statistic, it compares the observed counts with the counts we would expect to see
if the observed data perfectly obeyed the proposed distribution.
USES A SINGLE CATEGORICAL VARIABLE.
degrees of freedom - ANS k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule) - ANS expected value =
(column total)(row total) / overall total
If the distribution of the sleep quality is the same for the three age populations of university
students, what is the expected value of the test statistic? - ANS 2
If the distribution of sleep quality is the same for the three age populations of university
students, (i.e., if sleep quality is independent of age group) how would you determine the
expected count of young students reporting "good"quality sleep? [Set up the calculation you
would perform using values from the table of results; you do not need to complete the
computation. - ANS (𝟐𝟔 + 𝟒𝟖 + 𝟐𝟏) ∗ 𝟕𝟕/𝟐𝟗𝟎 across the row * total / overall total
The observed 𝜒 " test statistic was computed to be 4.73. The table belowshows the observed
counts for each joint outcome between age group andsleep quality, along with the expected
counts in parentheses. Which cell contributed the largest amount to the overall 𝜒 " = 4.73? The
least? Provide a2-3 sentence justification of your answer. - ANS The cell that contributes the
most is students in the old group reporting good sleep, since the difference between observed
and expected of ~6 is largest relative to the size of the expected count. The group with the
smallest contribution is the young students experiencing bad sleep, because the difference
between observed and expected counts is smallest relative to the expected count size for that
cell. We could also calculate the contributions foreach to verify the response above.
The p-value associated with the overall test statistic of 𝜒 " = 4.73 was 0.09395with estimated
effect size 𝑉7 = 0.1277. Which of the following statement(s)correctly interprets the p-value?
@COPYRIGHT ALL RIGHTS RESERVED PAGE 2 OF 10
