STT 231: Exam 3 Questions with 100% Correct
Answers
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
𝜒^2 test of independence
chi squared test of independence
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
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.
Right, positive
, What is standard deviation in chi-squared?
sqrt(2df)
chi squared goodness of fit
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
k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule)
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?
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.
Answers
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
𝜒^2 test of independence
chi squared test of independence
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
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.
Right, positive
, What is standard deviation in chi-squared?
sqrt(2df)
chi squared goodness of fit
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
k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule)
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?
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.
