Question

startibartfast, the king of tralfamadore, was an exceptionally tall man. he had a hypothesis that there’s a positive association in the land of tralfamadore between the length of a person’s first name and their height. he ordered his servants to collect information about each and every person in the land, regarding their height and the length of their first name. then, he analyzed the results and looked for trends in the data.
what type of statistical study did startibartfast use?
choose 1 answer:
sample study
experiment
observational study
is the study appropriate for the statistical questions it’s supposed to answer?
mark the most suitable choice.
choose 1 answer:
no, because he didn’t use randomization.
no, because the study doesn’t show whether a person’s name length affects their height.
no, because the hypothesis doesn’t make sense.
yes, because he adequately gathered relevant data.

Explanation:

First Question (Type of Statistical Study)

• A sample study involves analyzing a subset of a population, but here all people in the land were studied (census - like), so not a sample study.
• An experiment involves manipulating variables, but here no variables were manipulated (just collecting existing data on height and name length).
• An observational study is when we observe and collect data on variables without interfering, which matches collecting data on everyone's height and name length to look for trends.

• Option 1: Randomization is not needed for an observational study (it's more for experiments/surveys to reduce bias in selection), so this is incorrect.
• Option 2: An observational study can show association (correlation) but not causation (whether one variable affects the other). The study here is observational, so it can't show if name length affects height (only if they are associated), so this is a valid reason why it's not appropriate for answering if there's a causal relationship (though the question is about the statistical question it's supposed to answer - the hypothesis is about association, but even for association, the study collected all data, but the key issue is that observational studies can't prove causation, but the options: the best is that the study doesn't show causation (but the hypothesis is about association). Wait, re - evaluating: The study collected data on all people (census), so for association, it's appropriate? No, the options: Let's re - check. The fourth option says "Yes, because he adequately gathered relevant data" - he collected data on every person, so for looking at association (the hypothesis is about positive association), gathering all data (census) is appropriate for seeing if there's an association in the population. Wait, maybe I made a mistake earlier. Let's re - analyze:

The hypothesis is about a positive association in the land (the population). By collecting data on every person (census), he has the entire population's data, so he can analyze the association. So the study is appropriate because he gathered relevant data (height and name length) on the entire population.

Wait, let's check the options again:

• Option 1: Randomization is not required for an observational study of the entire population (since there's no sampling). So this is wrong.
• Option 2: The study is about association, not causation. The hypothesis is about association, so the study can show association (since it's the entire population). So this is wrong.
• Option 3: The hypothesis (positive association between name length and height) is a valid statistical hypothesis (even if it's a bit odd, it's a hypothesis about two variables), so this is wrong.
• Option 4: He collected data on every person in the land (relevant data: height and name length), so for answering the question about association in the land, gathering the entire population's data is appropriate.

So the correct answer is the fourth option: Yes, because he adequately gathered relevant data.

Answer:

C. Observational study

Second Question (Appropriateness of the Study)