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| Section | Objectives |
|---|---|
| Regression and Correlation | - Relationship analysis
|
| Probability | - Probability rules
|
| Probability Distributions | - Discrete distributions
|
| Statistical Inference | - Estimation
|
| Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 21
The dot plot illustrates the frequency of outdoor games played by students per week.
Which statement is true?
Answer: D
Explanation:
The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.
NEW QUESTION # 22
Two events mutually exclusive # P(A and B) = ?
Answer: B
Explanation:
Mutually exclusive events cannot happen at the same time. Therefore, the probability of their intersection is zero: P(A and B) = 0. For instance, on a single coin toss, the event "heads" and the event "tails" are mutually exclusive because a single toss cannot produce both outcomes. Option B applies to independent events when calculating the probability of both occurring, but mutually exclusive events with positive probabilities are not independent because one event prevents the other from occurring. Option C is used to find P(A or B) for mutually exclusive events, not P(A and B). Option D would mean both events always occur together, which directly contradicts mutual exclusivity. The word "and" is the key operator: it asks for overlap. Since mutually exclusive events have no overlap, the result is 0. Study Guide references/topics: mutually exclusive events, intersections, joint probability, addition rule.
NEW QUESTION # 23
A marketing analyst is studying the relationship between customer age groups, teens, adults, and seniors, and their preferred shopping methods, online and in-store.
Which numerical measure is most appropriate for this study?
Answer: D
Explanation:
This study involves two categorical variables: customer age group and preferred shopping method. Age group is categorical because customers are classified into groups such as teens, adults, and seniors. Shopping method is also categorical because customers are classified as preferring either online or in-store shopping.
When two categorical variables are analyzed together, conditional percentages are the most appropriate numerical summary because they describe how the distribution of one categorical variable changes within levels of another categorical variable. For example, the analyst could compute the percentage of teens who prefer online shopping, the percentage of adults who prefer online shopping, and the percentage of seniors who prefer online shopping. A five-number summary is used for quantitative data, not categorical data. Mean difference requires numerical measurements. A correlation coefficient measures the strength and direction of a linear relationship between two quantitative variables, so it is not appropriate here. References/topics from the Study Guide: two-variable categorical data, conditional percentages, categorical association, numerical summaries.
NEW QUESTION # 24
Given a normal distribution with a mean of 40 and a standard deviation of 6, what is the range that contains approximately 95% of the data?
Answer: C
Explanation:
For a normal distribution, the empirical rule states that approximately 95% of the data fall within two standard deviations of the mean. The mean is 40, and the standard deviation is 6. Two standard deviations equal 2 × 6
= 12. To construct the 95% interval, subtract and add 12 from the mean: 40 # 12 = 28 and 40 + 12 = 52.
Therefore, the range containing approximately 95% of the data is 28 to 52. Option D, 34 to 46, represents one standard deviation from the mean and corresponds to about 68% of the data. Option B, 22 to 58, represents three standard deviations from the mean and corresponds to approximately 99.7% of the data. Option C is not based on the stated standard deviation. The correct interval must be symmetric around the mean and extend exactly two standard deviations in each direction. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 25
A gardener records the length of a plant over a duration of 35 weeks. The scatterplot shows the data.
What is the relationship between length and time?
Answer: C
Explanation:
The scatterplot shows time on the horizontal axis and plant length on the vertical axis. As time increases, the plotted plant lengths also increase. This upward pattern indicates a positive relationship. The points are not randomly scattered; they follow a clear rising trend from approximately 3 inches at the beginning to more than 9 inches near the end of the observation period. Because the points cluster closely around an increasing pattern, the relationship is strong rather than weak. A negative relationship would require plant length to decrease as time increases, which is not shown. A weak positive relationship would show only a slight upward tendency with substantial scatter, but this graph shows a consistent increase across the weeks.
Therefore, the best description is a strong positive relationship between time and plant height or length.
References/topics from the Study Guide: scatterplots, association, positive correlation, strength of relationship.
NEW QUESTION # 26
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