IDA/Statistics
Annica Isaksson
September 9, 2008
732A28: Exercises on treatment of
nonresponse
1. In a school with 1,500 pupils, the school management initiates a survey of the pupils’ study
habits. An SRS of pupils of size n=300 is selected. Each selected pupil receives a mail
questionnaire with a number of questions. One of the questions is: “How many hours besides
your scheduled school time do you spend on your studies during an average week?”. 136
completed questionnaires are returned. For these respondents, the average number of hours is
8.2, with a standard deviation of 1.1. An SRS of 20 pupils is selected from the nonrespondents.
Each of these pupils are contacted by telephone and asked the questions in the questionnaire . In
this way, responses are obtained for all of them. For the 20 pupils in the follow-up, the average
number of hours is 6 with a standard deviation of 2.3. Use the two-phase sampling estimator in
Lohr section 8.3 to calculate a 95 % confidence interval for the average number of hours besides
scheduled school time that the pupils of the school spend on their studies during an average
week.
2. Consider again the fictitious survey of subscribers to a daily newspaper presented in the exercise
on multiple imputation. Assume that subscribers no 1,2, 4, 7, 9, 10, 14, 15, 17 and 20 are men
and the rest of them women. Using gender to form classes, calculate a weighting-class adjusted
point estimator (see Lohr Example 8.4) of the average monthly wage for all subscribers of the
newspaper.
3. (Continuation of Exercise 2. ) Assume that among all 5,000 subscribers of the newspaper, 3,500
are men and the rest are women. Calculate a poststratified point estimator (see Lohr Section
8.5.2) of the average monthly wage for all subscribers of the newspaper.
4. (Continuation of Exercise 2.) Using gender to form cells, use cell mean imputation (see Lohr
Section 8.6.2) to create a complete sample data set. Based on this data set, calculate a point
estimator of the average monthly wage for all subscribers of the newspaper.
5. (Continuation of Exercise 2.) Using gender to form cells, use random hot-deck imputation (see
Lohr Section 8.6.3) to create a complete sample data set. Based on this data set, calculate a point
estimator of the average monthly wage for all subscribers of the newspaper.