Data Science Statistical Concepts and Inference Questions and Answers

Question 1

A data scientist conducts an A/B test for a new website feature and calculates a p-value of 0.03. The chosen significance level (alpha) is 0.05. How should the p-value be interpreted?

Accepted Answer

There is a 3% probability of observing the current result, or a more extreme one, if the null hypothesis is true.

Answer

There is a 3% chance that the null hypothesis is true.

Answer

The result is not statistically significant, and the null hypothesis should not be rejected.

Answer

The new feature causes a 3% improvement in user engagement.

Question 2

A machine learning model is developed to predict customer churn. In testing, it is observed that the model performs exceptionally well on the training data but poorly on new, unseen data. Which of the following concepts does this scenario best describe?

Accepted Answer

The bias-variance tradeoff

Answer

High bias and low variance

Answer

Low bias and low variance

Answer

High bias and high variance

Question 3

A researcher calculates a 95% confidence interval for the average height of a certain population to be [170 cm, 180 cm]. Which of the following is the correct interpretation of this interval?

Accepted Answer

If we were to repeat the 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 population mean is between 170 cm and 180 cm.

Answer

95% of the individuals in the population have a height between 170 cm and 180 cm.

Answer

The sample mean has a 95% chance of being correct.

Question 4

In the context of hypothesis testing, what is a Type II error?

Accepted Answer

Failing to reject the null hypothesis when it is actually false.

Answer

Rejecting the null hypothesis when it is actually true.

Answer

The probability of observing the data given the null hypothesis is true.

Answer

Accepting the alternative hypothesis when it is false.

Question 5

According to the Central Limit Theorem, what happens to the sampling distribution of the sample mean as the sample size increases, regardless of the population's original distribution?

Accepted Answer

It approaches a normal distribution.

Answer

It approaches a uniform distribution.

Answer

Its variance increases.

Answer

It becomes more skewed.

Question 6

A company's data science team wants to test if a new marketing campaign led to a higher average daily website visit duration. The null hypothesis (H₀) is that the average duration is unchanged or lower, while the alternative hypothesis (H₁) is that the average duration is higher. After analysis, they fail to reject the null hypothesis. However, the campaign did, in fact, increase the average duration. What type of error has been made?

Accepted Answer

Type II Error

Answer

Sampling Error

Answer

Type I Error

Answer

Standard Error

A data scientist conducts an A/B test for a new website feature and calculates a p-value of 0.03.The chosen significance level (alpha) is 0.05.How should the p-value be interpreted?

A data scientist conducts an A/B test for a new website feature and calculates a p-value of 0.03.
The chosen significance level (alpha) is 0.05.
How should the p-value be interpreted?