Question bank

Pick an answer to see if you're right — with an explanation.

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StatisticsEasy

Which sampling method guarantees every city is represented in proportion to its size?

aConvenience sampling

bSnowball sampling

cStratified sampling

dSelf-selected online survey

StatisticsEasy

If you quadruple the sample size, what happens to the standard error of the mean?

aIt halves

bIt quarters

cIt doubles

dIt stays the same

StatisticsEasy

Ice-cream sales and AC sales are highly correlated across months. What is the most likely explanation?

aIce cream causes AC purchases

bAC purchases cause ice-cream sales

cThe correlation must be a data error

dA confounder: hot weather drives both

StatisticsEasy

Which test checks whether two categorical variables, such as city and payment method, are related?

aOne-way ANOVA

bChi-square test of independence

cPearson correlation

dPaired t-test

StatisticsMedium

Which statement correctly interprets a 95% confidence interval of [₹462, ₹510] for the mean bill?

a95% of bills lie between ₹462 and ₹510

bThere is a 95% probability the sample mean is in this range

cThe method produces intervals that contain the true mean in about 95% of repeated samples

dThe true mean is exactly ₹486

StatisticsMedium

A one-way ANOVA across four campaigns gives p = 0.002. What can you conclude?

aAt least one campaign mean differs; use a post-hoc test to find which

bAll four means are different from each other

cCampaign D is the best

dThe data are normally distributed

StatisticsMedium

What does this code estimate?

a = rng.beta(1 + 540, 1 + 11460, 100_000)
b = rng.beta(1 + 624, 1 + 11376, 100_000)
print((b > a).mean())

aThe p-value of a z-test

bThe required sample size

cThe posterior probability that B's conversion rate exceeds A's

dThe standard error of the difference

StatisticsMedium

In `smf.ols('sales ~ ad_spend + store_size', data=df).fit()`, the ad_spend coefficient is 2.0 (both in ₹ thousand). What does it mean?

aAd spend explains 2% of sales

bEach extra ₹1,000 of ads is associated with about ₹2,000 more sales, holding store size fixed

cAds double sales

dAds definitely cause ₹2,000 more sales in every store

StatisticsHard

An analyst checks an A/B test every morning and stops as soon as p < 0.05. Why is this a problem?

aIt makes the test less sensitive

bZ-tests cannot be run more than once

cIt reduces the sample ratio

dRepeated peeking inflates the false-positive rate well above 5%

StatisticsHard

A test planned a 50/50 split but recorded 51,800 vs 48,200 users. What should you do first?

aInvestigate a sample ratio mismatch before trusting any result

bDeclare the larger group the winner

cReweight the results and continue

dIgnore it; splits never match exactly