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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
| Topic 2: Probability Concepts | 20% | - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Probability rules, independent and dependent events - Discrete and continuous probability distributions |
| Topic 3: Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Observational studies vs experiments - Hypothesis testing framework and interpretation - Sampling methods and bias |
| Topic 4: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous |
| Topic 5: Correlation & Regression | 20% | - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation - Simple linear regression models |
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NEW QUESTION # 89
Z-score formula = ?
Answer: B
Explanation:
The z-score formula is z = (x # #)/#, where x is the observed value, # is the population mean, and # is the population standard deviation. A z-score standardizes a raw value by measuring how many standard deviations it lies above or below the mean. The numerator, x # #, gives the deviation from the mean. Dividing by # converts that deviation into standard deviation units. If z is positive, the value is above the mean. If z is negative, the value is below the mean. If z = 0, the value equals the mean. Option B incorrectly adds the value and mean, which does not measure deviation. Option C ignores the mean, and option D ignores the observed value entirely. The z-score is central for normal distribution calculations because it allows values from different scales to be compared using the standard normal distribution. Study Guide references/topics: z- scores, standard normal distribution, mean, standard deviation.
NEW QUESTION # 90
Regression intercept represents:
Answer: D
Explanation:
In a linear regression equation, usually written as # = b# + b#x, the intercept b# represents the predicted value of Y when X equals 0. It is the point where the regression line crosses the vertical axis. For example, if a model is # = 12 + 3x, the intercept 12 means the predicted response is 12 when x = 0. The slope, b#, is different; it represents the predicted change in Y for each one-unit increase in X. Correlation measures the strength and direction of a linear association, not the intercept. The mean is a measure of center for a variable and is not the same as a regression intercept. In applied settings, the intercept is meaningful only when X = 0 is within a realistic or relevant range of the data. Study Guide references/topics: linear regression, intercept interpretation, slope-intercept form, response prediction.
NEW QUESTION # 91
Chi-square test used for:
Answer: B
Explanation:
A chi-square test is commonly used to analyze categorical data, especially to determine whether two categorical variables are associated. In a chi-square test of independence, data are arranged in a contingency table, and observed cell counts are compared with expected cell counts under the assumption that the variables are independent. If the observed counts differ substantially from the expected counts, there is evidence of association between the categorical variables. For example, a chi-square test could examine whether voting preference is associated with age group or whether product preference differs by region.
Option B describes comparing means, which is typically handled by a t-test or related procedure. Option C refers to regression, which models relationships between variables, often involving quantitative outcomes.
Option D refers to variance, which is tested using different procedures depending on context. The key phrase is "categorical variables": chi-square methods work with counts in categories. Study Guide references/topics:
categorical data, contingency tables, chi-square test, association.
NEW QUESTION # 92
Probability it does NOT rain = 1 # 0.25 = ?
Answer: D
Explanation:
This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
# P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.
NEW QUESTION # 93
There are 12 cell phone charging cords available at a store for purchase. The length of each charging cord in inches is reflected as 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12, respectively.
What are the mean of these data?
Answer: B
Explanation:
The mean is the arithmetic average of a data set. To find it, add all values and divide by the number of values.
The cord lengths are 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12. Their sum is 84. Since there are 12 charging cords, divide 84 by 12 to obtain 7. Therefore, the mean cord length is 7 inches. This value represents the balance point of the distribution, not necessarily a value that must occur most often. In this data set, 6 appears most frequently, so 6 is the mode, but the question asks for the mean. Option B, 8, and option C, 9, are too large because several values are below 7. Option D, 6, identifies the most common value rather than the average. References/topics from the Study Guide: mean, measures of center, quantitative data, arithmetic average.
NEW QUESTION # 94
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