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| Section | Objectives |
|---|---|
| Probability Distributions | - Continuous distributions
|
| Regression and Correlation | - Relationship analysis
|
| Statistical Inference | - Hypothesis testing
|
| Descriptive Statistics | - Data visualization
|
| Probability | - Fundamental probability concepts
|
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NEW QUESTION # 10
What percent of data lies within 2 standard deviations of the mean in a normal distribution?
Answer: B
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 # 11
Probability of rolling sum = 12 = ?
Answer: D
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 # 12
A gardener records the length of a plant over a duration of 35 weeks. The scatterplot shows the data.
What is the relationship between length and time?
Answer: C
Explanation:
The scatterplot shows time on the horizontal axis and plant length on the vertical axis. As time increases, the plotted plant lengths also increase. This upward pattern indicates a positive relationship. The points are not randomly scattered; they follow a clear rising trend from approximately 3 inches at the beginning to more than 9 inches near the end of the observation period. Because the points cluster closely around an increasing pattern, the relationship is strong rather than weak. A negative relationship would require plant length to decrease as time increases, which is not shown. A weak positive relationship would show only a slight upward tendency with substantial scatter, but this graph shows a consistent increase across the weeks.
Therefore, the best description is a strong positive relationship between time and plant height or length.
References/topics from the Study Guide: scatterplots, association, positive correlation, strength of relationship.
NEW QUESTION # 13
Histogram vs bar chart:
Answer: C
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 # 14
Type I error # = 0.05 means:
Answer: D
Explanation:
The symbol # represents the significance level of a hypothesis test and is the probability of making a Type I error. A Type I error occurs when the null hypothesis is true but the test rejects it. Therefore, # = 0.05 means there is a 5% risk of rejecting a true null hypothesis under the testing procedure. This is often described as the false positive rate. Option B describes a Type II error, which involves failing to reject a false null hypothesis.
Option C is incorrect because a 5% significance level corresponds to a 95% confidence level in related confidence-interval contexts, not 5% confidence. Option D is unrelated; # is not a sample-size percentage.
The interpretation must connect # directly to the probability of incorrectly rejecting H# when H# is actually true. Study Guide references/topics: hypothesis testing, significance level, Type I error, null hypothesis.
NEW QUESTION # 15
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