FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers

Question 1

A data science team is conducting an A/B test on a new website feature.
After collecting data, they calculate a p-value of 0.03.
If their significance level (alpha) is set at 0.05, which of the following is the most accurate interpretation of the result?

Accepted Answer

The result is statistically significant, meaning there is sufficient evidence to reject the null hypothesis.

Answer

There is a 3% probability that the new feature has no effect on the outcome.

Answer

There is a 97% probability that the new feature is effective.

Answer

The result is not statistically significant, and the team should accept the null hypothesis.

Question 2

A data scientist is working with a dataset representing the daily number of users visiting a specific webpage. The distribution of this data is highly skewed to the right. To perform hypothesis testing on the average number of daily users, which statistical principle allows the use of a Z-test or t-test, provided the sample size is large enough?

Accepted Answer

The Central Limit Theorem

Answer

The Law of Large Numbers

Answer

Bayes' Theorem

Answer

The Empirical Rule

Question 3

Which of the following scenarios is best modeled by a Poisson distribution?

Accepted Answer

The number of customer service calls received by a call center in one hour.

Answer

The number of heads in 10 consecutive coin flips.

Answer

The time until the next customer arrives at a coffee shop.

Answer

The number of defective items in a batch of 100, where the probability of a defect is constant.

Question 4

In the context of statistical analysis, which statement best describes the fundamental difference between the Frequentist and Bayesian approaches?

Accepted Answer

Frequentists use probability to describe long-run frequencies of events, while Bayesians use it to quantify the degree of belief in a statement. [22]

Answer

Frequentist methods are only applicable to discrete data, whereas Bayesian methods are only for continuous data.

Answer

Bayesian statistics always yields a single point estimate for a parameter, while Frequentist statistics provides a probability distribution.

Answer

Frequentist statistics requires a prior distribution for parameters, while Bayesian statistics does not.

Question 5

A machine learning model is built to classify emails as 'spam' or 'not spam'. The model has a 99% accuracy rate. However, only 0.5% of all emails are actually spam. Why might accuracy be a misleading metric in this scenario?

Accepted Answer

A high accuracy can be achieved by a naive model that classifies every email as 'not spam'.

Answer

The model is likely overfitting to the training data.

Answer

The dataset is too small to draw any meaningful conclusions.

Answer

Accuracy is not a valid metric for classification problems.

Question 6

A data scientist calculates a 95% confidence interval for the average user engagement time on a new app feature to be [15.2 minutes, 18.6 minutes]. What is the correct interpretation of this interval?

Accepted Answer

If we were to repeat this sampling process many times, 95% of the calculated confidence intervals would contain the true population mean.

Answer

There is a 95% probability that the true average engagement time is between 15.2 and 18.6 minutes.

Answer

95% of all users have an engagement time between 15.2 and 18.6 minutes.

Answer

The sample mean engagement time has a 95% chance of being the true population mean.