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| Section | Weight | Objectives |
|---|---|---|
| Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots |
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Probability Concepts | 20% | - Normal distribution and empirical rule - Probability rules, independent and dependent events - Discrete and continuous probability distributions - Conditional probability and Venn diagrams |
| Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Confidence intervals for means/proportions - Observational studies vs experiments - Hypothesis testing framework and interpretation |
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NEW QUESTION # 127
A die is rolled twice. Probability of rolling two sixes?
Answer: A
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 # 128
The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
Assuming a normal distribution, which two values encompass 95% of the data?
Answer: B
Explanation:
For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 129
95% confidence interval for mean = (45, 55). Which statement is correct?
Answer: C
Explanation:
A 95% confidence interval provides a plausible range of values for an unknown population mean based on sample data. The interval (45, 55) means the method used to construct the interval captures the true population mean in approximately 95% of repeated samples under the same conditions. In practical exam language, the correct interpretation is that the population mean is estimated to lie within the interval with 95% confidence. Option B states the midpoint of the interval, 50, but the question asks for the correct confidence interval interpretation, not just the center. Option C is incorrect because the population mean is not always the upper endpoint. Option D is imprecise because once an interval is computed, it is fixed; the confidence level refers to the long-run success rate of the procedure, not a changing probability attached to that exact fixed interval. Study Guide references/topics: confidence intervals, population mean, point estimate, margin of error.
NEW QUESTION # 130
A researcher has collected information on students from a school. The researcher wants to display the ethnic groups represented in the school.
Which pair of graphs both display data in this manner?
Answer: B
Explanation:
Ethnic group is a categorical variable because it classifies students into named groups rather than measuring a numerical quantity. Categorical data are commonly displayed with bar graphs or pie charts. A bar graph shows the frequency or relative frequency of each category using separate bars, making it easy to compare group sizes. A pie chart shows how the whole student population is divided among categories, making it useful for displaying proportions or percentages. Therefore, the correct pair is bar graph and pie chart. A box plot is used for quantitative data and summarizes values using quartiles and a median, so it is not appropriate for ethnic categories. A line graph is typically used to show change over time or ordered numerical trends. A histogram is used for distributions of quantitative data grouped into intervals, not named categories. Since the goal is to display category membership, both selected graphs must support categorical frequency or percentage displays. References/topics from the Study Guide: categorical data displays, bar graphs, pie charts, relative frequency.
NEW QUESTION # 131
A road safety research group wants to enhance road safety by analyzing the stopping distance of a car at different speeds. The group has recorded their data in the following scatterplot.
What is true about the outlier in the scatterplot?
Answer: A
Explanation:
An outlier is a data point that does not follow the general pattern of the remaining data. In this scatterplot, most points show a clear increasing relationship: as speed increases, stopping distance also increases. The main cluster follows a smooth upward trend, with stopping distances gradually rising as speed increases. One point, however, is far above the rest of the pattern. That point is located at approximately 40 mph and 560 feet, making it unusually high compared with the expected stopping distance at that speed. This is why option D correctly identifies the outlier. Option A describes a low-speed point that fits the lower end of the trend.
Option B describes a high-speed point near the upper end of the general pattern, not an unusual deviation.
Option C describes a point around 30 mph and 190 feet, which lies within the main cluster of observations.
The outlier is not merely an extreme x-value or y-value; it is unusual relative to the trend. References/topics from the Study Guide: scatterplots, outliers, bivariate data, association patterns.
NEW QUESTION # 132
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