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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Descriptive Statistics | - Data visualization
|
| Probability | - Probability rules
|
| Probability Distributions | - Continuous distributions
|
| Statistical Inference | - Hypothesis testing
|
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NEW QUESTION # 32
A person has a .5 probability of taking a train to work, a .3 probability of carpooling, and a .2 probability of walking. The probability of being late is .2 when taking the train, .1 when carpooling, and .05 when walking.
What is the probability of taking the train and being on time, or walking and being on time?
Answer: A
Explanation:
This problem combines complements, joint probabilities, and addition of mutually exclusive outcomes. First compute the probability of taking the train and being on time. The probability of being late when taking the train is .2, so the probability of being on time by train is 1 # .2 = .8. Thus, P(train and on time) = .5 × .8 = .40.
Next compute the probability of walking and being on time. The probability of being late when walking is .
05, so the probability of being on time while walking is 1 # .05 = .95. Thus, P(walking and on time) = .2 × .95
= .19. Since a person cannot both take the train and walk as the selected commuting mode, these outcomes are mutually exclusive. Add the two results: .40 + .19 = .59. References/topics from the Study Guide:
complements, conditional probability, joint probability, addition rule.
NEW QUESTION # 33
Dataset: 5, 7, 7, 10. Standard deviation?
Answer: B
Explanation:
The standard deviation measures the typical distance of data values from the mean. For the dataset 5, 7, 7, 10, the mean is (5 + 7 + 7 + 10) ÷ 4 = 29 ÷ 4 = 7.25. The deviations from the mean are #2.25, #0.25, #0.25, and
2.75. Squaring these deviations gives 5.0625, 0.0625, 0.0625, and 7.5625. The sum of squared deviations is
12.75. If treated as a sample, the variance is 12.75 ÷ 3 = 4.25, and the sample standard deviation is #4.25 #
2.06. If rounded using the answer set provided, the closest available value is 2.16. The key conceptual point is that standard deviation cannot be 0 unless all values are identical, and it is not as large as 3 because the observations are relatively close to the mean. Study Guide references/topics: mean, variance, standard deviation, spread of data.
NEW QUESTION # 34
Type I error = ?
Answer: D
Explanation:
A Type I error occurs when a statistical test rejects the null hypothesis even though the null hypothesis is actually true. This is often described as a false positive. In practical terms, the test concludes that there is an effect, difference, or relationship when none truly exists under the null condition. The probability of committing a Type I error is denoted by #, the significance level, often set at 0.05. Option B describes a Type II error, where the test fails to reject a false null hypothesis. Option C is not an error at all. Option D is too general; Type I error is not a data-entry issue but a formal decision error in hypothesis testing. The defining phrase is "reject H# when true." Study Guide references/topics: hypothesis testing, Type I error, null hypothesis, significance level.
NEW QUESTION # 35
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 # 36
The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
Assuming a normal distribution, which two values encompass 95% of the data?
Answer: C
Explanation:
For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 37
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