Statistical Inference and Hypothesis Testing Flashcards
6 cards from real DSE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Statistical Inference and Hypothesis Testing flashcards as text
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?
Answer: Reject the null hypothesis; the evidence suggests a statistically significant difference in click-through rates.
The p-value (0.04) is less than the significance level α (0.05). This means the observed result is unlikely to have occurred by random chance alone if the null hypothesis were true. Therefore, we reject the null hypothesis and conclude there is a statistically significant effect.
In hypothesis testing, which of the following describes a Type I error?
Answer: Rejecting a true null hypothesis.
A Type I error, also known as a 'false positive,' occurs when the null hypothesis is rejected even though it is actually true. The probability of committing a Type I error is denoted by the significance level, alpha (α).
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?
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.
The 95% confidence level refers to the reliability of the estimation method, not a specific interval. It means that if we repeated the experiment or sampling many times, 95% of the intervals we create would capture the true, unknown population parameter.
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?
Answer: Analysis of Variance (ANOVA)
ANOVA is used to compare the means of three or more independent groups. A t-test is only suitable for comparing the means of two groups. Using multiple t-tests would inflate the probability of a Type I error.
In the context of hypothesis testing, what does the statistical power of a test represent?
Answer: The probability of correctly rejecting a false null hypothesis.
Statistical power is the probability that the test will correctly detect a true effect when one exists. In other words, it is the probability of avoiding a Type II error (failing to reject a false null hypothesis). Power is denoted as 1 - β.
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?
Answer: A one-tailed test, because the hypothesis is directional.
A one-tailed test is used when the alternative hypothesis specifies a direction (e.g., greater than or less than). Since the team is specifically testing for an *improvement* (an increase in scores), a one-tailed test is appropriate. A two-tailed test would be used if they were testing for *any* difference, either positive or negative.