alleryStart learning →The mean of the sampling distribution of sample means equals:
AThe size of the sample
BThe standard error
CThe population mean
DZero in every case
Answer & Solution
Correct answer: C. The population mean
1. Averaging many sample means recovers the value being estimated.
2. The law of large numbers says the mean of the sample tends to get closer and closer to the population mean as samples grow.
3. So the sampling distribution is centred on the population mean itself.
4. Its spread, not its centre, is what changes with sample size.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_
Keep practising The Central Limit Theorem
Browse all The Central Limit Theorem questions for AP Statistics, or explore more Statistics topics.
Related questions
Complete the sampling rulesWhich has the smaller standard error?True or false: sampling distributionsMatch each sampling ideaThe standard error appears in calculator routines as a parameter alongside:Comparing the law of large numbers with the central limit theorem, the law of large numberA population that is already close to normal needs which sample size for the theorem to apRecognising a central limit theorem problem means spotting a question about: