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WGU Applied-Probability-and-Statistics Exam Syllabus Topics:

SectionWeightObjectives
Topic 1: Descriptive Statistics25%- Graphical displays: histograms, boxplots, scatterplots
- Types of data: categorical, discrete, continuous
- Measures of center: mean, median, mode
- Measures of spread: range, IQR, variance, standard deviation
Topic 2: Correlation & Regression20%- Predictions and limitations of regression
- Correlation coefficient and interpretation
- Interpreting slope, intercept, and R-squared
- Simple linear regression models
Topic 3: Probability Concepts20%- Conditional probability and Venn diagrams
- Normal distribution and empirical rule
- Discrete and continuous probability distributions
- Probability rules, independent and dependent events
Topic 4: Inferential Statistics & Study Design20%- Confidence intervals for means/proportions
- Observational studies vs experiments
- Hypothesis testing framework and interpretation
- Sampling methods and bias
Topic 5: Basic Numeracy & Algebra15%- Linear equations, inequalities, graphing functions
- Exponents, roots, and basic formulas
- Arithmetic operations, fractions, decimals, percentages

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WGU Applied Probability and Statistics (FZO1 C955) 認定 Applied-Probability-and-Statistics 試験問題 (Q156-Q161):

質問 # 156
Type II error = ?

正解:B

解説:
A Type II error occurs when the null hypothesis is false, but the test fails to reject it. Many introductory materials describe this as "accepting H# when false," although the more precise statistical wording is "failing to reject H#." This is a false negative: a real effect, difference, or relationship exists, but the test does not detect enough evidence to conclude it. For example, if a new teaching method truly improves scores but the test fails to find significance, the result is a Type II error. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is a correct test decision, not an error. Option D is invalid because Type II error is a defined concept. The probability of Type II error is #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.


質問 # 157
A spinner is divided into four equal sections labeled A, B, C, and D.
What is the sample space for this experiment?

正解:C

解説:
The sample space of a probability experiment is the complete set of all possible outcomes. In this experiment, the spinner has four equal sections labeled A, B, C, and D. Since one spin can land on exactly one of those four labeled sections, the possible outcomes are A, B, C, and D. Therefore, the sample space is {A, B, C, D}.
Option A incorrectly adds E, which is not listed as a section on the spinner. Option B groups labels into combined outcomes, but the experiment is a single spin, not a two-part or paired event. Option C uses numerical labels, but the spinner sections are identified by letters, not numbers. Equal section size affects the probability of each outcome, making each outcome have probability 1/4, but it does not change the sample space itself. References/topics from the Study Guide: probability experiments, outcomes, sample space, equally likely events.


質問 # 158
Type II error # is:

正解:A

解説:
A Type II error occurs when the null hypothesis is false but the test fails to reject it. Many introductory answer choices phrase this as "accept H# when false," though the more technically careful wording is "fail to reject H# when false." This is a false negative: the real effect or difference exists, but the test does not detect sufficient evidence. The probability of a Type II error is denoted #. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is incorrect because 1 # # is not #; # is the Type I error probability, while 1 # # is statistical power. Option D is too vague and does not identify a formal hypothesis- testing error. The defining condition for Type II error is missing a real effect by failing to reject a false null hypothesis. Study Guide references/topics: Type II error, beta, hypothesis testing, statistical power.


質問 # 159
A university surveys faculty and students to determine support for a new campus recycling initiative.
The results of the survey are shown in the following 2 × 2 contingency table:

Which statement is true?

正解:B

解説:
This problem compares conditional percentages across two groups. For faculty members, 40 out of 50 support the recycling initiative, so the faculty support rate is 40/50 = 0.80, or 80%. For students, 200 out of 500 support the initiative, so the student support rate is 200/500 = 0.40, or 40%. Comparing 80% and 40% shows that faculty members are twice as likely as students to support the initiative. This is not a slight difference; it is a large difference of 40 percentage points. Therefore, the correct statement is that faculty members are much more likely than students to support the recycling initiative. The table contains two categorical variables: group type and recycling opinion. Conditional percentages are the appropriate numerical tool because the goal is to compare support within each group. References/topics from the Study Guide:
contingency tables, two-way categorical data, conditional percentages, comparative proportions.


質問 # 160
A fitness center owner notices that gym attendance increases as the number of daylight hours increases. The owner calculates a correlation coefficient between daylight hours and gym attendance of r = 0.72.
Based on this information, what can be concluded?

正解:B

解説:
The correlation coefficient r measures the direction and strength of a linear association between two quantitative variables. Since r = 0.72 is positive, the relationship is positive: as daylight hours increase, gym attendance tends to increase. The value 0.72 also indicates a moderately strong to strong linear association because it is closer to 1 than to 0. However, correlation alone does not establish causation. Even though daylight hours and gym attendance move together, other variables could influence attendance, such as weather, seasonal routines, work schedules, or fitness promotions. Therefore, the valid conclusion is that there is a positive association, not a proven causal relationship. Options A and B are incorrect because they describe a negative relationship, which conflicts with the positive correlation coefficient. Option D overstates the evidence by claiming causation. References/topics from the Study Guide: correlation coefficient, positive association, linear relationship, correlation versus causation.


質問 # 161
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