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| Section | Objectives |
|---|---|
| Probability Distributions | - Continuous distributions
|
| Probability | - Probability rules
|
| Descriptive Statistics | - Data summarization
|
| Statistical Inference | - Hypothesis testing
|
| Regression and Correlation | - Relationship analysis
|
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NEW QUESTION # 136
Probability of rolling sum = 12 = ?
Answer: B
Explanation:
Rolling two six-sided dice produces 36 equally likely ordered outcomes. A sum of 12 can occur only when both dice show 6, giving the single ordered pair (6, 6). Since there is exactly 1 favorable outcome out of 36 total outcomes, the probability is 1/36. This is structurally similar to rolling a sum of 2, where only (1, 1) works. Option B, 1/6, is much too large and would apply to one specified face on one die. Option C, 2/36, would require two different ordered outcomes, but no pair other than (6, 6) sums to 12. Option D, 1/12, also overstates the probability. Extreme sums such as 2 and 12 are least likely because they have only one possible ordered combination. Study Guide references/topics: sample spaces, dice sums, theoretical probability, equally likely outcomes.
NEW QUESTION # 137
Histogram vs bar chart:
Answer: B
Explanation:
A histogram and a bar chart both use bars, but they display different types of data. A histogram is used for quantitative numerical data grouped into intervals, such as ages, weights, test scores, or commute times. The bars represent continuous or ordered numeric ranges, and the bars usually touch to show that the scale is continuous. A bar chart is used for categorical data, such as favorite sport, political party, product type, or survey response category. The bars are separated because the categories are distinct labels rather than continuous intervals. Option B reverses the correct uses. Option C is incorrect because the graphs are not the same even though both contain bars. Option D is invalid because option A states the standard distinction.
Correct graph selection depends on identifying whether the variable is categorical or quantitative. Study Guide references/topics: histograms, bar charts, categorical data, quantitative data displays.
NEW QUESTION # 138
Given a normal distribution with a mean of 40 and a standard deviation of 6, what is the range that contains approximately 95% of the data?
Answer: C
Explanation:
For a normal distribution, the empirical rule states that approximately 95% of the data fall within two standard deviations of the mean. The mean is 40, and the standard deviation is 6. Two standard deviations equal 2 × 6
= 12. To construct the 95% interval, subtract and add 12 from the mean: 40 # 12 = 28 and 40 + 12 = 52.
Therefore, the range containing approximately 95% of the data is 28 to 52. Option D, 34 to 46, represents one standard deviation from the mean and corresponds to about 68% of the data. Option B, 22 to 58, represents three standard deviations from the mean and corresponds to approximately 99.7% of the data. Option C is not based on the stated standard deviation. The correct interval must be symmetric around the mean and extend exactly two standard deviations in each direction. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 139
A dataset: 4, 8, 12, 16, 20. Mean = ?
Answer: D
Explanation:
The mean is the arithmetic average of a data set. To compute it, add all values and divide by the number of observations. For the dataset 4, 8, 12, 16, and 20, the sum is 4 + 8 + 12 + 16 + 20 = 60. There are 5 values, so the mean is 60 ÷ 5 = 12. The mean represents the balance point of the data. This dataset is evenly spaced around 12: 4 and 20 are equally distant from 12, and 8 and 16 are equally distant from 12. That symmetry supports the computed result. Option A, 10, is too low because it does not account for the higher values 16 and 20. Option C, 14, is too high, and option D is one of the data values but not the average. The correct answer is 12. Study Guide references/topics: mean, arithmetic average, measures of center, quantitative data.
NEW QUESTION # 140
Chi-square test used for:
Answer: D
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 # 141
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