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| Section | Objectives |
|---|---|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Regression and Modeling | - Linear Relationships
|
| Probability Theory | - Probability Distributions
|
>> WGU Applied-Probability-and-Statistics Certification Questions <<
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NEW QUESTION # 33
Boxplot shows:
Answer: D
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 # 34
Correlation coefficient r = #0.9 indicates:
Answer: A
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. It ranges from #1 to 1. A value close to #1 indicates a strong negative linear relationship, meaning that as one variable increases, the other tends to decrease in a highly consistent linear pattern. Since r = #0.9 is very close to #1, the relationship is strong and negative. Option B is incorrect because the sign is negative, not positive. Option C identifies the direction correctly but understates the strength; #0.9 is not weak. Option D would correspond to r near 0, where there is little or no linear association. A scatterplot associated with r = #0.9 would show points clustered closely around a downward- sloping line. This does not prove causation; it describes linear association only. Study Guide references
/topics: correlation coefficient, negative association, strength of relationship, scatterplots.
NEW QUESTION # 35
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 # 36
A sociologist is investigating the relationship between educational level, high school, bachelor's, master's, and doctorate, and annual income.
How should this study be classified?
Answer: B
Explanation:
This study contains two variables: educational level and annual income. Educational level is categorical because it places individuals into named groups, such as high school, bachelor's, master's, and doctorate.
Although these categories have a natural order, they are still categories rather than measured numerical quantities. Annual income is quantitative because it is measured numerically and can be analyzed using arithmetic summaries such as mean, median, range, and standard deviation. Therefore, the study is classified as categorical-to-quantitative. This classification is important because it determines appropriate statistical displays and summaries. For example, side-by-side box plots or group means could be used to compare annual income across education levels. A categorical-to-categorical study would involve two label-based variables, such as education level and employment sector. A quantitative-to-quantitative study would involve two numerical variables, such as income and years of experience. References/topics from the Study Guide:
categorical variables, quantitative variables, two-variable data classification, comparative summaries.
NEW QUESTION # 37
Standard deviation measures:
Answer: A
Explanation:
Standard deviation measures the spread, variability, or dispersion of data values around the mean. A small standard deviation indicates that the data values are clustered closely around the mean, while a large standard deviation indicates that the values are more widely dispersed. It is calculated from deviations from the mean, squared deviations, variance, and then the square root of variance. Standard deviation is not a measure of central tendency; measures of central tendency include the mean, median, and mode. It is also not a probability, although it is used in probability distributions such as the normal distribution. Frequency refers to how often a value or category occurs, which is summarized with tables, bar charts, histograms, or dot plots.
The standard deviation is essential because it quantifies how consistent or variable a dataset is. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.
NEW QUESTION # 38
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