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| Section | Weight | Objectives |
|---|---|---|
| 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 |
| Probability Concepts | 20% | - Discrete and continuous probability distributions - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events |
| Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Confidence intervals for means/proportions - Observational studies vs experiments - Hypothesis testing framework and interpretation |
| Correlation & Regression | 20% | - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation - Simple linear regression models |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
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NEW QUESTION # 98
A single ball is drawn from an opaque bag that contains red, blue, and green balls. The probability of drawing a red ball is .3, and the probability of drawing a blue ball is .6.
What is the probability of drawing a green ball?
Answer: B
Explanation:
The probabilities of all possible outcomes in a sample space must sum to 1. In this experiment, the bag contains only red, blue, and green balls, so these three outcomes exhaust the sample space. The probability of drawing a red ball is 0.3, and the probability of drawing a blue ball is 0.6. Their combined probability is 0.3 +
0.6 = 0.9. The remaining probability must belong to drawing a green ball. Therefore, P(green) = 1 # 0.9 = 0.1.
This can also be viewed as a complement problem: green is the complement of drawing either red or blue when those are the only other colors available. Option B repeats the red probability, option C would make the total probability exceed 1, and option D is the combined probability of red or blue rather than green.
References/topics from the Study Guide: probability sum rule, complements, sample space, mutually exclusive outcomes.
NEW QUESTION # 99
Null hypothesis for a new drug shows no effect. True statement?
Answer: D
Explanation:
The null hypothesis represents the default claim or baseline assumption in hypothesis testing. For a new drug, a typical null hypothesis states that the drug has no effect, no difference from placebo, or no improvement over the existing standard. The testing process begins by assuming the null hypothesis is true, then evaluates whether the sample evidence is strong enough to reject it. Therefore, the correct statement is that researchers assume no effect until evidence suggests otherwise. This does not mean the drug is proven ineffective; it means the burden of evidence lies with demonstrating an effect. Option B is the alternative hypothesis, not the null. Option C overstates the conclusion because failing to reject the null does not prove the drug has no effect. Option D is false because this type of claim is testable using experimental data and statistical inference.
Study Guide references/topics: null hypothesis, alternative hypothesis, hypothesis testing, statistical evidence.
NEW QUESTION # 100
Probability of drawing king or queen from deck = ?
Answer: C
Explanation:
A standard deck contains 52 cards. There are 4 kings and 4 queens, one of each rank in each suit. The event is drawing a king or a queen. Since a single card cannot be both a king and a queen, these two events are mutually exclusive. Therefore, the number of favorable outcomes is 4 + 4 = 8. The probability is favorable outcomes divided by total outcomes: 8/52. This fraction can be simplified to 2/13, but the answer choice provides the unsimplified correct form. Option B, 4/52, counts only kings or only queens, not both. Option C,
1/13, is equivalent to 4/52 and again represents one rank only. Option D, 1/26, is too small and does not match the count of favorable cards. The word "or" signals that both qualifying ranks should be included. Study Guide references/topics: card probability, mutually exclusive events, addition rule, sample space.
NEW QUESTION # 101
The average lifespan of a dalmatian is 11.5 years, with a standard deviation of 1.5 years.
What are the two values between which 95% of the data falls for the average lifespan of a dalmatian, assuming a normal distribution?
Answer: B
Explanation:
For a normal distribution, the empirical rule states that approximately 95% of observations lie within two standard deviations of the mean. The mean lifespan is 11.5 years, and the standard deviation is 1.5 years. Two standard deviations equal 2 × 1.5 = 3.0 years. Therefore, the interval containing approximately 95% of the data is found by subtracting and adding 3.0 years to the mean: 11.5 # 3.0 = 8.5 and 11.5 + 3.0 = 14.5. The resulting interval is 8.5 years to 14.5 years. Option C, 10.0 to 13.0, represents one standard deviation from the mean and would correspond to about 68% of the data. Options A and D are not centered correctly at the proper two-standard-deviation distance. The correct interval must be symmetric around the mean and use two standard deviations. References/topics from the Study Guide: normal distributions, empirical rule, standard deviation, measures of spread.
NEW QUESTION # 102
Two dice rolled, probability of both even = ?
Answer: A
Explanation:
A standard six-sided die has three even outcomes: 2, 4, and 6. Thus, the probability that one die lands on an even number is 3/6 = 1/2. When two dice are rolled, the outcomes are independent because the result of one die does not affect the other. Therefore, the probability that both dice are even is 1/2 × 1/2 = 1/4.
Equivalently, there are 36 ordered outcomes for two dice. The even-even outcomes are formed from 3 even choices on the first die and 3 even choices on the second die, giving 3 × 3 = 9 favorable outcomes. Then 9/36 simplifies to 1/4. Option B gives the probability of one die being even, not both. Options C and D do not match the count or multiplication rule. Study Guide references/topics: independent events, dice probability, multiplication rule, sample space.
NEW QUESTION # 103
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