I have data from a questionnaire asking about how they felt on a few variables (for example quality of sleep) before and after taking a fitness training course. There are 140+ responses.
However, there are several (maybe about 10) respondents who didn't answer the basic questions about their age and/or gender, although they did answer the ordinal scale questions that came later in the questionnaire (for example quality of sleep).
I would like to ask two questions about such missing values.
Would it be statistically acceptable if I keep such observations when I am analyzing only one variable at a time (for example a hypothesis test about only the variable quality of sleep)?
Could these missing values (age, gender) in the results be remedied with some imputation method, or I must delete all the observations with missing gender and/or age when I go on to jointly analyze at least one of these variables with one/several other answers in the questionnaire?