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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Probability | - Fundamental probability concepts
|
| Descriptive Statistics | - Data visualization
|
| Statistical Inference | - Hypothesis testing
|
| Probability Distributions | - Continuous distributions
|
>> WGU Applied-Probability-and-Statistics New Question <<
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NEW QUESTION # 127
Mean = 50, SD = 5, n = 25. Standard error = ?
Answer: D
Explanation:
The standard error of the mean measures the expected sampling variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size: SE = s / #n. In this question, the standard deviation is 5 and the sample size is 25. Therefore, SE = 5 / #25 = 5 / 5 = 1. The mean of 50 identifies the center of the sample distribution but is not directly used in the standard error calculation.
Option B, 5, is the standard deviation, not the standard error. Option C, 25, is the sample size. Option D, 0.2, would result from incorrectly dividing 5 by 25 rather than by the square root of 25. The distinction between standard deviation and standard error is important: standard deviation describes spread among individual observations, while standard error describes spread among sample means. Study Guide references/topics:
standard error, standard deviation, sample size, sampling distributions.
NEW QUESTION # 128
Histogram is best for:
Answer: A
Explanation:
A histogram is used to display the frequency distribution of quantitative numerical data, especially continuous data grouped into intervals or bins. For example, a histogram can show the distribution of heights, test scores, commute times, or weights. Each bar represents a numerical interval, and the height of the bar represents how many observations fall within that interval. Unlike a bar chart, the bars in a histogram usually touch because the intervals form a continuous numerical scale. Option B is incorrect because categorical data are better displayed with a bar chart or pie chart. Option C is incorrect because a scatterplot displays the relationship between two quantitative variables, not the frequency distribution of one variable. Option D is incorrect because a boxplot summarizes median, quartiles, spread, and outliers rather than showing detailed frequency counts. The correct graph for continuous numerical frequency is a histogram. Study Guide references/topics:
histograms, quantitative data, frequency distributions, graphical displays.
NEW QUESTION # 129
Binomial distribution parameters = ?
Answer: C
Explanation:
A binomial distribution is defined by two parameters: n and p. The parameter n is the fixed number of trials, and p is the probability of success on each trial. The model applies when trials are independent, each trial has two possible outcomes, and p remains constant. For example, if X is the number of heads in 10 fair coin flips, then X follows a binomial distribution with n = 10 and p = 0.5. Option B, #, is the parameter of a Poisson distribution, used for counts of events over intervals. Option C, # and #, commonly describes a normal distribution, where # is the mean and # is the standard deviation. Option D is incorrect because the binomial model has a precise parameter structure. Identifying n and p is essential before calculating binomial probabilities or expected value. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete probability.
NEW QUESTION # 130
Probability it does NOT rain = 1 # 0.25 = ?
Answer: A
NEW QUESTION # 131
Type I error # = 0.05 means:
Answer: B
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 # 132
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