DSE - Data Science Statistical Inference and Hypothesis Testing Questions and Answers

Question 1

An A/B test was conducted to determine if changing a website's call-to-action button from green to blue would increase the click-through rate.
The null hypothesis stated there is no difference in the rates.
The test resulted in a p-value of 0.04.
If the pre-determined significance level (alpha) was 0.05, what is the correct interpretation?

Accepted Answer

Reject the null hypothesis; the evidence suggests a statistically significant difference in click-through rates.

Answer

The probability that the null hypothesis is true is 4%.

Answer

Fail to reject the null hypothesis, as the result is not statistically significant.

Answer

There is a 96% probability that the blue button is more effective.

Question 2

In hypothesis testing, which of the following describes a Type I error?

Accepted Answer

Rejecting a true null hypothesis.

Answer

Failing to reject a false null hypothesis.

Answer

Correctly rejecting a false null hypothesis.

Answer

Correctly failing to reject a true null hypothesis.

Question 3

A data scientist calculates a 95% confidence interval for the average daily screen time of users on a new mobile app, resulting in an interval of [35.2 minutes, 39.8 minutes]. Which of the following is the most accurate interpretation of this result?

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 for daily screen time.

Answer

95% of all users have a daily screen time between 35.2 and 39.8 minutes.

Answer

There is a 95% probability that the true average daily screen time for all users is between 35.2 and 39.8 minutes.

Answer

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

Question 4

A retail company wants to test if there is a statistically significant difference in the average transaction value among customers using three different payment methods (Credit Card, Debit Card, Mobile Pay). Which statistical test is most appropriate for this analysis?

Accepted Answer

Analysis of Variance (ANOVA)

Answer

Paired t-test

Answer

Independent two-sample t-test

Answer

Chi-squared test

Question 5

In the context of hypothesis testing, what does the statistical power of a test represent?

Accepted Answer

The probability of correctly rejecting a false null hypothesis.

Answer

The probability of observing a result at least as extreme as the sample, assuming the null hypothesis is true.

Answer

The probability of incorrectly rejecting a true null hypothesis.

Answer

The maximum p-value allowed to declare a result as statistically significant.

Question 6

A research team wants to test if a new employee wellness program *improves* productivity scores. The null hypothesis is that the program has no effect on productivity. The team is only interested in whether the program leads to an increase, not a decrease. Which type of test is most appropriate?

Accepted Answer

A one-tailed test, because the hypothesis is directional.

Answer

A chi-squared test, because the outcome is categorical.

Answer

A two-tailed test, to see if there is any difference in either direction.

Answer

An F-test, to compare the variances of the two groups.