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

SectionObjectives
Statistical Inference- Hypothesis Testing (Introductory Level)
  • 1. p-values interpretation
    • 2. Null vs alternative hypothesis
      - Estimation and Confidence Intervals
      • 1. Confidence interval interpretation
        • 2. Point estimates
          Probability Theory- Fundamental Probability Concepts
          • 1. Basic probability rules
            • 2. Conditional probability
              • 3. Independent vs dependent events
                - Probability Distributions
                • 1. Normal distribution
                  • 2. Binomial distribution basics
                    Regression and Modeling- Linear Relationships
                    • 1. Slope and intercept interpretation
                      • 2. Simple linear regression
                        Descriptive Statistics- Single Variable Data Analysis
                        • 1. Measures of central tendency (mean, median, mode)
                          • 2. Data visualization (histograms, box plots)
                            • 3. Measures of dispersion (variance, standard deviation, range)
                              - Two Variable Data Analysis
                              • 1. Correlation
                                • 2. Outliers and relationships
                                  • 3. Scatter plots interpretation

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                                    WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q93-Q98):

                                    NEW QUESTION # 93
                                    Dataset: 3, 6, 9. Median?

                                    Answer: B

                                    Explanation:
                                    The median is the middle value of a data set after the values are placed in ascending order. The dataset is 3, 6,
                                    9, which is already ordered from least to greatest. Since there are three observations, the median is the second value, because one value lies below it and one value lies above it. Therefore, the median is 6. The median is a measure of center and is especially useful when data may be skewed or contain outliers because it depends on position rather than the magnitude of every value. The mean for this dataset is also 6, since (3 + 6 + 9) ÷ 3 =
                                    6, but the question specifically asks for the median. Options B and C are not values in the dataset, and option D is the minimum value, not the middle. Study Guide references/topics: median, ordered data, measures of central tendency, descriptive statistics.


                                    NEW QUESTION # 94
                                    Z-score negative #

                                    Answer: B

                                    Explanation:
                                    A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.


                                    NEW QUESTION # 95
                                    Type II error occurs when:

                                    Answer: C

                                    Explanation:
                                    A Type II error occurs when the null hypothesis is false but the statistical test fails to reject it. In many answer choices, this is expressed as "accepting the null when false," though the more precise language is "failing to reject the null." This error is a false negative: the test misses a real effect, difference, or relationship. For example, if a medication truly improves recovery but a study fails to detect sufficient evidence of improvement, that is a Type II error. Option B describes a Type I error, which occurs when a true null hypothesis is rejected. Option C is not an error. Option D is too vague; statistical decision errors refer specifically to incorrect conclusions about hypotheses, not ordinary data-entry mistakes. The probability of a Type II error is denoted #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.


                                    NEW QUESTION # 96
                                    Regression slope indicates:

                                    Answer: A

                                    Explanation:
                                    In a linear regression equation, the slope represents the predicted change in the response variable Y for each one-unit increase in the explanatory variable X. In slope-intercept form, # = b# + b#x, the slope is b#. For example, if a regression equation predicts cost as # = 25 + 4x, the slope 4 means the predicted cost increases by 4 units for each additional unit of x. The intercept, b#, is the predicted value of Y when X = 0, so option B describes a different component. R² measures the proportion of variation in Y explained by the regression model, not the rate of change. Correlation measures strength and direction of linear association, but it is not the same as the slope because it is unitless and standardized. The slope is the operational rate of change in the model. Study Guide references/topics: linear regression, slope interpretation, response variable, explanatory variable.


                                    NEW QUESTION # 97
                                    t-test used when:

                                    Answer: A

                                    Explanation:
                                    A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
                                    That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.


                                    NEW QUESTION # 98
                                    ......

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