Inferential Statistics PCAD-31 Practice Questions (Page 3)

Questions 11–15

1. 11foundation · easy

   To construct a bootstrap sampling distribution for the sample mean, what steps are performed?

   • ACompute the mean of the original sample and then add random noise to create a distribution
   • BSplit the original sample into multiple equal parts and compute the mean of each part
   • CDraw many bootstrap samples from the original data, compute the mean of each, and collect these means
   • DTake one large sample from the population and compute the mean once
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2. 12foundation · easy

   Which metric is commonly used to evaluate the classification performance of a logistic regression model?

   • AMean squared error and root mean squared error
   • BR-squared and adjusted R-squared
   • CF1-score and Gini coefficient only
   • DAccuracy, precision, recall, and area under the ROC curve (AUC)
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4. 13expert · hard

   A researcher has a sample of 25 observations and wants a confidence interval for the population mean. The data are approximately normal. The researcher is considering using either a t-interval or a bootstrap percentile interval. Which statement best describes the trade-off?

   • AThe t-interval will always be wider than the bootstrap interval
   • BThe t-interval is preferred because it is exact under normality, while the bootstrap interval is approximate
   • CThe bootstrap interval is preferred because it does not require any assumptions
   • DBoth intervals will be identical in all cases
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5. 14expert · hard

   A data analyst fits a linear regression model with 20 predictors on a dataset of 100 observations. The model achieves an R-squared of 0.95, but when applied to a new validation dataset, the R-squared drops to 0.40. Which issue is most likely?

   • AExtrapolation beyond the range of the predictors
   • BThe outcome variable is not normally distributed
   • COverfitting the training data
   • DMulticollinearity among the predictors
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6. 15foundation · easy

   What does a 95% bootstrap confidence interval for a population parameter represent?

   • AA range that has a 95% probability of containing the sample statistic
   • BAn interval that is expected to contain the true parameter value in about 95% of repeated applications of the procedure
   • CA range that contains exactly 95% of the original sample data
   • DA guarantee that the true parameter lies within the interval
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