MS-DS Master of Data science Statistical Inference Concepts Questions and Answers

Question 1

A data scientist at an e-commerce company runs an A/B test on a new checkout button design.
The null hypothesis is that the new button has no effect on the conversion rate.
After analyzing the results, they obtain a p-value of 0.03.
Assuming a significance level (alpha) of 0.05, what is the correct interpretation of this p-value?

Accepted Answer

If the null hypothesis were true, there would be a 3% probability of observing a difference in conversion rates at least as extreme as the one detected.

Answer

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

Answer

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

Answer

The new button caused a 3% increase in the conversion rate.

Question 2

A data scientist calculates a 95% confidence interval for the average user session duration to be [150, 170] seconds. Which of the following is the correct interpretation of this interval?

Accepted Answer

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

Answer

There is a 95% probability that the true population mean session duration is between 150 and 170 seconds.

Answer

95% of all individual user session durations fall between 150 and 170 seconds.

Answer

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

Question 3

A pharmaceutical company conducts a clinical trial for a new drug. The null hypothesis (H0) is that the drug has no effect. The alternative hypothesis (H1) is that the drug has a positive effect. They conclude the drug is effective (reject H0), but in reality, it is not. In the context of hypothesis testing, what type of error has been made?

Accepted Answer

Type I Error

Answer

Type II Error

Answer

Standard Error

Answer

Sampling Error

Question 4

Which of the following statements best describes the primary utility of the Central Limit Theorem (CLT) for a data scientist conducting statistical inference?

Accepted Answer

It allows for the use of statistical tests assuming a normal distribution for the sample mean's sampling distribution, even if the population distribution is non-normal, given a sufficiently large sample size.

Answer

It guarantees that any dataset will follow a normal distribution if the sample size is large enough.

Answer

It states that the standard deviation of a sample will always equal the standard deviation of the population.

Answer

It is used to eliminate all sources of sampling error in an experiment.

Question 5

In the context of designing an experiment, what does the 'statistical power' of a hypothesis test represent?

Accepted Answer

The probability of correctly rejecting the null hypothesis when it is in fact false.

Answer

The probability of making a Type I error, also known as alpha.

Answer

The minimum sample size required to achieve a statistically significant result.

Answer

The effect size of the observed phenomenon.

Question 6

A data scientist has a sample of 100 customer satisfaction scores. The distribution of these scores is unknown and appears to be heavily skewed. They need to estimate the 95% confidence interval for the median satisfaction score. Which statistical technique is most appropriate?

Accepted Answer

Bootstrapping

Answer

Two-sample t-test

Answer

Analysis of Variance (ANOVA)

Answer

Chi-squared test