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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Simple linear regression models |
| Topic 2: Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments - Sampling methods and bias |
| Topic 3: Descriptive Statistics | 25% | - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode |
| Topic 4: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
| Topic 5: Probability Concepts | 20% | - Discrete and continuous probability distributions - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events |
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NEW QUESTION # 155
Mean = 100, SD = 15, z = 2. Value = ?
Answer: A
Explanation:
A z-score expresses how many standard deviations a value lies above or below the mean. The formula is z = (x # #)/#. To solve for the raw value x, rearrange the formula: x = # + z#. Here, the mean # is 100, the standard deviation # is 15, and z = 2. Substitute these values: x = 100 + 2(15) = 100 + 30 = 130. Therefore, the raw value is 130. This means the value is two standard deviations above the mean. Option B, 115, would correspond to z = 1. Option C, 125, is not exactly two standard deviations above 100 when # = 15. Option D,
110, is less than one standard deviation above the mean. The correct value must add two full standard deviations to the mean. Study Guide references/topics: z-scores, standardization, normal distribution, raw score conversion.
NEW QUESTION # 156
Boxplot shows:
Answer: A
Explanation:
A boxplot displays the distribution of a quantitative variable using the five-number summary and potential outliers. The main features are the median, first quartile, third quartile, lower whisker, upper whisker, and any marked outliers. The box extends from Q1 to Q3 and represents the interquartile range, which contains the middle 50% of the data. The line inside the box marks the median. Whiskers show the spread of non-outlier values, depending on the graphing convention. Option B is incorrect because a boxplot does not show only the mean; many boxplots do not display the mean at all. Option C is incorrect because variance is a numerical measure of spread, not a standard direct feature of a boxplot. Option D is incorrect because a boxplot is not a probability model. It is a descriptive display for summarizing center, spread, and unusual observations. Study Guide references/topics: boxplots, median, quartiles, interquartile range, outliers.
NEW QUESTION # 157
Z-test used when:
Answer: C
Explanation:
A z-test for a population mean is used when the population standard deviation # is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic # hypothesized parameter) divided by the standard error. Knowing # allows the standard error to be computed using #/#n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when # is unknown. Option D is unrelated to the classic z- test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.
NEW QUESTION # 158
In a normal distribution, 95% of data lies within:
Answer: A
Explanation:
For a normal distribution, the empirical rule states that approximately 68% of data fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations. The notation ±2 SD means two standard deviations below the mean to two standard deviations above the mean, or # # 2# to # + 2#. Therefore, the interval containing about 95% of normally distributed observations is ±2 standard deviations. Option B corresponds to approximately 68%, not
95%. Option C corresponds to approximately 99.7%, and option D extends beyond the standard empirical- rule benchmarks. This concept is central when estimating the typical spread of bell-shaped data, such as test scores, biological measurements, or repeated measurement errors. The correct answer is ±2 SD because it matches the 95% portion of the 68-95-99.7 rule. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.
NEW QUESTION # 159
Uniform distribution 0-5: P(X < 3) = ?
Answer: B
Explanation:
For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length.
The total interval length is 5 # 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval's probability equals its length divided by the total length.
Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of
5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary.
The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references
/topics: uniform distribution, continuous probability, interval length, probability density.
NEW QUESTION # 160
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