Statistics CERTIFIED-DATA-SCIENCE-PRACTITIONER Practice Questions (Page 2)

Questions 6–10

1. 6foundation · medium

   Which statistical test is appropriate for comparing the means of two independent groups when the data are normally distributed?

   • AMann-Whitney U test
   • BIndependent samples t-test
   • CPaired t-test
   • DChi-square test
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2. 7expert · hard · select all that apply

   A data scientist constructs a 95% confidence interval for the mean delivery time and obtains [22.5, 27.5] minutes. Which of the following statements are correct? Select all that apply.

   • AThe interval width would likely decrease if the sample size were increased.
   • BThere is a 95% probability that the true population mean lies between 22.5 and 27.5 minutes.
   • CIf the same sampling procedure were repeated many times, about 95% of the computed intervals would contain the true population mean.
   • D95% of individual delivery times fall between 22.5 and 27.5 minutes.
   • EA two-sided hypothesis test of whether the mean equals 25 minutes would not be rejected at the 0.05 significance level.
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4. 8foundation · medium

   If the normality assumption is violated for a t-test, what is an appropriate corrective action?

   • AIncrease the sample size to force normality
   • BUse a non-parametric test such as the Mann-Whitney U test
   • CIgnore the violation because t-tests are robust to all violations
   • DUse a chi-square test instead
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5. 9application · medium

   A data scientist plans to use an independent two-sample t-test to compare the mean income of two customer segments. Before running the test, the scientist checks the distributions and finds that one segment's income is heavily right-skewed while the other is roughly normal, and the variances are very different. What should the scientist do?

   • AProceed with the standard t-test because the central limit theorem protects the test with large samples.
   • BUse Welch's t-test, which does not assume equal variances, and consider a non-parametric alternative if the skew is severe.
   • CUse a paired t-test because the segments are compared on the same variable.
   • DRemove outliers from the skewed segment to make it normal, then run the standard t-test.
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6. 10expert · hard

   A clinical trial with 500 patients per group finds a statistically significant reduction in blood pressure (p = 0.01) with a mean difference of 2 mmHg and a 95% confidence interval of [0.5, 3.5] mmHg. The FDA requires a minimum clinically meaningful reduction of 5 mmHg. What should the data scientist conclude?

   • AThe treatment is clinically meaningful because the confidence interval is entirely above 0.
   • BThe result is inconclusive because the confidence interval is too narrow.
   • CThe treatment is not clinically meaningful because the upper bound of the confidence interval (3.5 mmHg) is below the 5 mmHg threshold.
   • DThe treatment is effective because the p-value is below 0.05 and the confidence interval excludes 0.
   Reveal Solution Discussion Select an answer first