Central Limit Theorem (CLT) and Normal Distribution Questions
Understand the CLT: when you take multiple random samples and calculate their means, those sample means are normally distributed (bell-shaped) even if the underlying data isn't. Know that normal distribution is parameterized by mean and standard deviation. Appreciate why this matters: it allows you to estimate population characteristics from samples and construct confidence intervals.
HardTechnical
0 practiced
You ran 100 hypothesis tests across different customer segments using CLT-based z-tests and obtained several significant p-values. Discuss why multiple comparisons are a concern, and explain at least two methods for controlling family-wise error rate or false discovery rate. Indicate which method you would choose for an exploratory analysis vs a regulatory report.
MediumTechnical
0 practiced
You run an A/B test to compare conversion rates: control has 200 conversions out of 10,000 visitors, treatment has 250 conversions out of 10,000 visitors. Using the CLT (normal approximation), compute the z-score and two-sided p-value for the difference in proportions. Then discuss whether the normal approximation is appropriate here and any caveats a data scientist should communicate.
EasyTechnical
1 practiced
List and briefly explain the core assumptions typically stated when invoking the CLT for sample means in applied work. For each assumption provide a practical check or diagnostic a data scientist could run on their dataset (for example, how to check independence or finite variance practically).
MediumTechnical
0 practiced
Derive the standard error formula for the difference of two independent sample means and explain assumptions required to use a normal approximation for hypothesis testing of the difference. Provide a short example with sample means 50 and 53, sample sds 10 and 12, and n1 = n2 = 40 to compute a test statistic.
MediumTechnical
0 practiced
Explain the finite population correction (FPC) factor and when it should be applied. Given a population of N = 5,000 users and a sample without replacement of n = 2,500 users, show how the standard error of the sample mean changes when applying FPC, assuming sample sd = 20.
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