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| Section | Objectives |
|---|---|
| Topic 1: Descriptive Statistics | - Data visualization
|
| Topic 2: Regression and Correlation | - Relationship analysis
|
| Topic 3: Probability | - Probability rules
|
| Topic 4: Probability Distributions | - Discrete distributions
|
| Topic 5: Statistical Inference | - Estimation
|
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NEW QUESTION # 131
A commuter has a .4 probability of taking the bus to work, a .4 probability of driving a car, and a .2 probability of cycling. The probability of being late is .15 when taking the bus, .05 when driving a car, and .1 when cycling.
What is the probability of taking the bus and being on time, or driving a car and being on time?
Answer: C
Explanation:
This item requires multiplying conditional probabilities and then adding mutually exclusive outcomes.
"Taking the bus and being on time" means the commuter takes the bus and is not late. Since the probability of being late by bus is .15, the probability of being on time by bus is 1 # .15 = .85. Therefore, P(bus and on time)
= .4 × .85 = .34. For driving, the probability of being late is .05, so the probability of being on time is 1 # .05
= .95. Therefore, P(car and on time) = .4 × .95 = .38. Because a commuter cannot both take the bus and drive a car on the same trip, the events are mutually exclusive. Add the two joint probabilities: .34 + .38 = .72. The cycling information is not used because the question asks only about bus-on-time or car-on-time outcomes.
References/topics from the Study Guide: probability rules, complements, conditional probability, mutually exclusive events.
NEW QUESTION # 132
Sample correlation r = 0.6. R² = ?
Answer: C
Explanation:
The coefficient of determination, R², is obtained by squaring the correlation coefficient r in simple linear regression. Here, r = 0.6, so R² = (0.6)² = 0.36. This means that 36% of the variability in the response variable is explained by the linear relationship with the explanatory variable. The remaining 64% of variability is not explained by that linear model and may be due to other variables, random variation, measurement error, or nonlinear structure. Option B gives the correlation itself, not its square. Option C would come from squaring
0.4, not 0.6. Option D would imply a perfect explanatory relationship, which would require |r| = 1. The value of R² is always between 0 and 1 and is commonly interpreted as a proportion of explained variation. Study Guide references/topics: correlation, coefficient of determination, regression, explained variation.
NEW QUESTION # 133
A teacher compares the test scores of two classes using a box plot.
What is true about the median test scores?
Answer: B
Explanation:
A box plot displays the five-number summary, including the median, which is shown by the vertical line inside each box. In the exhibit, the median for Class A is positioned at approximately 65, while the median for Class B is positioned at approximately 80. The difference is therefore 80 # 65 = 15 points. Since Class A's median is lower, the correct interpretation is that the median test score of Class A is 15 points less than that of Class B. This comparison uses a categorical grouping variable, class, and a quantitative response variable, test score. The box plot is appropriate because it allows the distributions of two groups to be compared visually using medians, quartiles, ranges, and potential spread. Options A, B, and D do not match the median locations shown by the center lines in the boxes. References/topics from the Study Guide: box plots, median, five- number summary, comparing distributions.
NEW QUESTION # 134
In a game, a coin is tossed, and a spinner with 8 equal spaces numbered 1 through 8 is spun.
What is the probability of getting heads on the coin and a number less than 3 on the spinner?
Answer: C
NEW QUESTION # 135
Variance formula = ?
Answer: A
Explanation:
The sample variance formula is s² = #(x# # x#)² / (n # 1). In this formula, x# represents each data value, x# is the sample mean, and n is the sample size. The expression x# # x# gives each value's deviation from the mean. Squaring the deviations prevents negative and positive deviations from canceling and emphasizes larger departures. Dividing by n # 1 gives the sample variance, using degrees of freedom to correct bias when estimating population variance from a sample. Option B is the formula for the sample mean, not variance.
Option C squares the mean and does not measure spread. Option D resembles part of the standard deviation process but omits division by n # 1 and is not the variance formula. Variance is foundational because standard deviation is the square root of variance. Study Guide references/topics: variance, sample variance formula, mean deviations, measures of spread.
NEW QUESTION # 136
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