1. Email outreach efforts. A medical research group is recruiting people to complete short surveys about their medical history. For example, one survey asks for information on a person’s family history in regards to cancer. Another survey asks about what topics were discussed during the person’s last visit to a hospital. So far, as people sign up, they complete an average of just 4 surveys, and the standard deviation of the number of surveys is about 2.2. The research group wants to try a new interface that they think will encourage new enrollees to complete more surveys, where they will randomize each enrollee to either get the new interface or the current interface. How many new enrollees do they need for each interface to detect an effect size of 0.5 surveys per enrollee, if the desired power level is 80%?
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1. Email outreach efforts. A medical research group is recruiting people to complete short surveys
about their medical history. For example, one survey asks for information on a person’s family
history in regards to cancer. Another survey asks about what topics were discussed during the
person’s last visit to a hospital. So far, as people sign up, they complete an average of just
4 surveys, and the standard deviation of the number of surveys is about 2.2. The research group
wants to try a new interface that they think will encourage new enrollees to complete more surveys,
where they will randomize each enrollee to either get the new interface or the current interface.
How many new enrollees do they need for each interface to detect an effect size of 0.5 surveys per
enrollee, if the desired power level is 80%?
2. Work hours and education. The General Social Survey collects data on demographics, education,
and work, among many other characteristics of US residents. Using ANOVA, we can consider
educational attainment levels for all 1,172 respondents at once. Below are the distributions of
hours worked by educational attainment and relevant summary statistics that will be helpful in
carrying out this analysis.
Educational attainment
Less than HS HS Jr Coll Bachelor’s Graduate Total
Mean 38.67 39.6 41.39 42.55 40.85 40.45
SD 15.81 14.97 18.1 13.62 15.51 15.17
n 121 546 97 253 155 1,172
Hours worked per week
Less than HS HS Jr Coll Bachelor's Graduate
0
20
40
60
80
1(a) Write hypotheses for evaluating whether the average number of hours worked varies across
the five groups.
(b) Check conditions and describe any assumptions you must make to proceed with the test.
(c) Below is part of the output associated with this test. Fill in the empty cells.
5. Child care hours. The China Health and Nutrition Survey aims to examine the effects of the
health, nutrition, and family planning policies and programs implemented by national and local
governments. It, for example, collects information on number of hours Chinese parents spend taking
care of their children under age 6. The side-by-side box plots below show the distribution of this
variable by educational attainment of the parent. Also provided below is the ANOVA output for
comparing average hours across educational attainment categories.
2Child care hours
Primary school Lower middle school Upper middle school Technical or vocational College
0
50
100
150
Df Sum Sq Mean Sq F value Pr(>F)
education 4 4142.09 1035.52 1.26 0.2846
Residuals 794 653047.83 822.48
(a) Write the hypotheses for testing for a difference between the average number of hours spent
on child care across educational attainment levels.
(b) What is the conclusion of the hypothesis test?
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