I. The probability that a person with the disease tests positive is $$0.90$$. II. The probability that a person without the disease tests positive is $$0.05$$. III. By applying Bayes' Theorem, the probability that a person who tests positive actually has the disease is given by $$\frac{0.05 \times 0.05}{0.05 \times 0.05 + 0.95 \times 0.90}$$, which is approximately 0.0029. Which of the above statements is/are true?

If X and Y are independent discrete random variables with standard deviations σX = 3 and σY = 4, which expression correctly gives the standard deviation of 2X - 3Y?

The probability of a student answering a multiple-choice question correctly by guessing is 0.25. If a student guesses on questions until getting one correct, what is the expected number of questions the student will need to answer?

A quality control inspector examines computer chips until finding a defective one. If 8% of chips are defective, what is the variance of the number of chips that need to be examined?

A student answers 10 multiple-choice questions by guessing randomly. Each question has 4 options with only one correct answer. What is the probability that the student gets between 2 and 4 correct answers, inclusive?

A pharmaceutical company is testing a new drug against a placebo. They are concerned about the psychological effect of patients knowing which treatment they're receiving. Which experimental design element is most critical to address this concern?

A study comparing three different teaching methods found statistically significant differences in test scores (ANOVA, p = 0.001). Under what condition would this statistical significance NOT provide evidence that the teaching methods caused the differences in test scores?

A researcher wants to study the relationship between sleep habits and academic performance among college students. She stands outside the library and surveys the first 50 students who enter. Why is this method of data collection problematic?

In a prospective cohort study, researchers tracked 1,000 individuals over 10 years and found that those who reported higher stress levels had increased incidence of certain autoimmune disorders. Which of the following represents the most appropriate generalization from this study?

A researcher is conducting an experiment to determine the effect of different levels of a new fertilizer on plant growth. The researcher uses three different concentrations of the fertilizer: 0%, 5%, and 10%. Each concentration is applied to a separate group of plants. What is the explanatory variable in this experiment, and how many treatments are being tested?

In a study of 200 students categorized by gender and study habits, what does a marginal frequency of 75 in the 'female' column indicate?

In which scenario might the y-intercept of a regression line lack logical interpretation?

What does a funnel shape in a residual plot indicate about the model?

A researcher studying the relationship between gender and choice of academic major collected data from 500 students. Out of 250 female students, 100 chose STEM as their major. What is the conditional relative frequency of females majoring in STEM?

In what way does the coefficient of determination (R-squared) reflect the strength of a linear relationship between variables in a regression model?

Which of the following is an example of computing the standard deviation from a dataset?

Data sets A and B have the same mean and median, but data set A has standard deviation of 12 and IQR of 15, while data set B has standard deviation of 8 and IQR of 20. Which statement is most accurate?

Which of the following is NOT a quantitative variable?

The IQR for a dataset is 15. After adding a constant c to each value in the dataset, the IQR becomes 15. After multiplying each original value by c, the IQR becomes 45. What is the value of c?

Which of the following is a quantitative variable?