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| Section | Weight | Objectives |
|---|---|---|
| Correlation & Regression | 20% | - Simple linear regression models - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Sampling methods and bias - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions |
| Probability Concepts | 20% | - Normal distribution and empirical rule - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Conditional probability and Venn diagrams |
| Descriptive Statistics | 25% | - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode |
| Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions |
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NEW QUESTION # 15
Empirical probability = ?
Answer: B
Explanation:
Empirical probability is probability determined from observed data rather than from a purely theoretical model. It is calculated by dividing the number of times an event actually occurs by the total number of trials or observations. For example, if a basketball player makes 72 free throws in 100 attempts, the empirical probability of a made free throw is 72/100 = 0.72. This differs from theoretical probability, which is derived from known equally likely outcomes, such as rolling a 3 on a fair six-sided die. It also differs from a guess or subjective estimate because empirical probability requires actual recorded evidence. The term "uniform" describes a distribution in which outcomes or intervals have equal probability, not the basis for empirical probability. Since the question asks for the definition of empirical probability, the correct selection is observed data. Study Guide references/topics: empirical probability, relative frequency, observed outcomes, probability interpretation.
NEW QUESTION # 16
95% CI = 50 ± 2. SE = ?
Answer: A
Explanation:
A confidence interval has the structure estimate ± margin of error. The margin of error is calculated as critical value × standard error. For a 95% confidence interval using the normal approximation, the critical value is approximately 1.96, often rounded to 2 in introductory settings. The interval is given as 50 ± 2, so the margin of error is 2. Using the approximate 95% critical value of 2, we solve 2 = 2 × SE, giving SE = 1. More exactly, using 1.96 gives SE = 2/1.96 # 1.02, which rounds to 1. Option B confuses the margin of error with the standard error. Option C is too large, and option D would produce a margin of error near 1 under a 95% critical value. The correct standard error is approximately 1. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.
NEW QUESTION # 17
Two independent events: P(A) = 0.3, P(B) = 0.2. P(A or B) = ?
Answer: D
Explanation:
For two events, the general addition rule is P(A or B) = P(A) + P(B) # P(A and B). Because A and B are independent, their joint probability is P(A and B) = P(A)P(B). Here, P(A) = 0.3 and P(B) = 0.2, so P(A and B)
= 0.3 × 0.2 = 0.06. Then P(A or B) = 0.3 + 0.2 # 0.06 = 0.44. The subtraction is necessary because the overlap, where both A and B occur, is counted twice when adding P(A) and P(B). Option A, 0.5, incorrectly adds the two probabilities without correcting for overlap. Option B gives the probability of both events, not either event. Option D is unrelated to the addition rule. Study Guide references/topics: independent events, addition rule, multiplication rule, union of events.
NEW QUESTION # 18
In a class of 40 students, the following data were collected on their favorite sport:
* Soccer: 10 students
* Basketball: 15 students
* Tennis: 5 students
* Swimming: 10 students
What is the relative frequency of students whose favorite sport is not basketball?
Answer: B
Explanation:
Relative frequency is the proportion of observations in a category compared with the total number of observations. The class has 40 students. Basketball accounts for 15 students, so the number of students whose favorite sport is not basketball is 40 # 15 = 25. The relative frequency is therefore 25/40. Dividing gives
0.625. This means 62.5% of the class selected a sport other than basketball. The same result can be found by adding the non-basketball categories directly: soccer 10, tennis 5, and swimming 10, giving 10 + 5 + 10 = 25 students. Option A, 0.25, corresponds to 10 out of 40 and would represent soccer or swimming alone. Option B, 0.50, corresponds to 20 out of 40. Option D, 0.75, would imply 30 students, which is too high. References
/topics from the Study Guide: relative frequency, categorical data, frequency tables, proportions.
NEW QUESTION # 19
A die is rolled twice. Probability of rolling two sixes?
Answer: C
Explanation:
Rolling a standard six-sided die twice creates two independent events. The probability of rolling a six on the first roll is 1/6 because there is one favorable outcome, six, out of six equally likely outcomes. The probability of rolling a six on the second roll is also 1/6. Because the outcome of the first roll does not affect the outcome of the second roll, the multiplication rule for independent events applies. Thus, P(six and six) = 1/6 × 1/6 = 1
/36. Another way to verify the result is to list the sample space: two die rolls produce 6 × 6 = 36 equally likely ordered outcomes. Only one outcome, (6, 6), satisfies the condition of two sixes. Therefore, the probability is
1 favorable outcome out of 36 total outcomes. Study Guide references/topics: independent events, multiplication rule, sample space, theoretical probability.
NEW QUESTION # 20
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