STT 231 EXAM 3 QUESTIONS AND CORRECT ANSWERS 100%
VERIFIED!!! ALREADY GRADED A+
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 - (answer)𝜒^2 test of independence
chi squared test of independence - (answer)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 - (answer)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. - (answer)Right,
positive
What is standard deviation in chi-squared? - (answer)sqrt(2df)
chi squared goodness of fit - (answer)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.
, STT 231 EXAM 3 QUESTIONS AND CORRECT ANSWERS 100%
VERIFIED!!! ALREADY GRADED A+
degrees of freedom - (answer)k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule) - (answer)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? - (answer)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. - (answer)(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. - (answer)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? Select all correct
answers - (answer)The p-value of 𝑝 = 0.09395 is the probability of witnessing a test statistic of 𝜒 " = 4.73
, or something higher, under the assumption 𝐻? is true.
Suppose the amount of data that was collected for the test was much larger(for instance, 𝑛 = 290 or 𝑛 =
580) but the observed proportions of the sample that fell within each cell remained the same. Consider
how each of the following quantities would change
VERIFIED!!! ALREADY GRADED A+
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 - (answer)𝜒^2 test of independence
chi squared test of independence - (answer)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 - (answer)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. - (answer)Right,
positive
What is standard deviation in chi-squared? - (answer)sqrt(2df)
chi squared goodness of fit - (answer)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.
, STT 231 EXAM 3 QUESTIONS AND CORRECT ANSWERS 100%
VERIFIED!!! ALREADY GRADED A+
degrees of freedom - (answer)k-1 k being categories
Computing expected counts for a two-way table (Cross-product rule) - (answer)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? - (answer)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. - (answer)(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. - (answer)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? Select all correct
answers - (answer)The p-value of 𝑝 = 0.09395 is the probability of witnessing a test statistic of 𝜒 " = 4.73
, or something higher, under the assumption 𝐻? is true.
Suppose the amount of data that was collected for the test was much larger(for instance, 𝑛 = 290 or 𝑛 =
580) but the observed proportions of the sample that fell within each cell remained the same. Consider
how each of the following quantities would change
