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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Probability Concepts | 20% | - Discrete and continuous probability distributions - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events |
| Topic 2: Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions - Observational studies vs experiments - Sampling methods and bias |
| Topic 3: Descriptive Statistics | 25% | - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots |
| Topic 4: Correlation & Regression | 20% | - Simple linear regression models - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation - Predictions and limitations of regression |
| Topic 5: 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 # 85
What percent of data lies within 2 standard deviations of the mean in a normal distribution?
Answer: C
Explanation:
For a normal distribution, the empirical rule, also called the 68-95-99.7 rule, describes how data are distributed around the mean. Approximately 68% of observations fall within 1 standard deviation of the mean, approximately 95% fall within 2 standard deviations, and approximately 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 2 standard deviations, so the correct value is 95%. This interval is written as # # 2# to # + 2#, where # is the mean and # is the standard deviation.
Option B corresponds to one standard deviation, not two. Option C is an imprecise version of the three- standard-deviation rule, and option D has no standard empirical-rule interpretation in this context. This rule is frequently used to estimate ranges in bell-shaped distributions. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.
NEW QUESTION # 86
Dataset: 3, 5, 7, 9, 11. Median = ?
Answer: D
Explanation:
The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.
NEW QUESTION # 87
Null hypothesis for a new drug shows no effect. True statement?
Answer: B
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 # 88
Variance formula = ?
Answer: A
Explanation:
The sample variance formula is s² = #(x# # x#)² / (n # 1). In this formula, x# represents each data value, x# is the sample mean, and n is the sample size. The expression x# # x# gives each value's deviation from the mean. Squaring the deviations prevents negative and positive deviations from canceling and emphasizes larger departures. Dividing by n # 1 gives the sample variance, using degrees of freedom to correct bias when estimating population variance from a sample. Option B is the formula for the sample mean, not variance.
Option C squares the mean and does not measure spread. Option D resembles part of the standard deviation process but omits division by n # 1 and is not the variance formula. Variance is foundational because standard deviation is the square root of variance. Study Guide references/topics: variance, sample variance formula, mean deviations, measures of spread.
NEW QUESTION # 89
Mean of Poisson # = 5 = ?
Answer: C
Explanation:
For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.
NEW QUESTION # 90
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