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| Section | Objectives |
|---|---|
| Probability Theory | - Probability Distributions
|
| Regression and Modeling | - Linear Relationships
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Descriptive Statistics | - Two Variable Data Analysis
|
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NEW QUESTION # 64
Type II error = ?
Answer: D
Explanation:
A Type II error occurs when the null hypothesis is false, but the test fails to reject it. Many introductory materials describe this as "accepting H# when false," although the more precise statistical wording is "failing to reject H#." This is a false negative: a real effect, difference, or relationship exists, but the test does not detect enough evidence to conclude it. For example, if a new teaching method truly improves scores but the test fails to find significance, the result is a Type II error. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is a correct test decision, not an error. Option D is invalid because Type II error is a defined concept. The probability of Type II error is #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.
NEW QUESTION # 65
Random variable X = number of heads in 4 coin flips #
Answer: A
Explanation:
The random variable X counts the number of heads obtained in 4 coin flips. Since it is a count, it can take only specific whole-number values: 0, 1, 2, 3, or 4. It cannot take fractional values such as 2.5 heads. A random variable with countable possible outcomes is classified as discrete. This situation also fits a binomial framework because there is a fixed number of independent trials, each trial has two outcomes, and the probability of heads remains constant for a fair coin. A continuous random variable, by contrast, can take any value over an interval, such as time, weight, or height. The number of heads is not measured on a continuum; it is counted. Therefore, the correct classification is discrete. Study Guide references/topics: discrete random variables, binomial setting, coin-flip outcomes, probability distributions.
NEW QUESTION # 66
Correlation coefficient r = #0.9 indicates:
Answer: D
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. It ranges from #1 to 1. A value close to #1 indicates a strong negative linear relationship, meaning that as one variable increases, the other tends to decrease in a highly consistent linear pattern. Since r = #0.9 is very close to #1, the relationship is strong and negative. Option B is incorrect because the sign is negative, not positive. Option C identifies the direction correctly but understates the strength; #0.9 is not weak. Option D would correspond to r near 0, where there is little or no linear association. A scatterplot associated with r = #0.9 would show points clustered closely around a downward- sloping line. This does not prove causation; it describes linear association only. Study Guide references
/topics: correlation coefficient, negative association, strength of relationship, scatterplots.
NEW QUESTION # 67
A teacher plots the test scores of a class using the box plot.
What is true about the test scores?
Answer: A
Explanation:
A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.
NEW QUESTION # 68
A study recorded the number of hours participants spent on exercise per week: 3 participants exercised for 1 hour, 6 participants exercised for 2 hours, 4 participants exercised for 3 hours, and 2 participants exercised for
4 hours.
Which type of graph would best represent the frequency of exercise hours?
Answer: C
Explanation:
The data describe frequencies for a single variable: weekly exercise duration. Each duration, 1 hour through 4 hours, has an associated count of participants. A bar chart is the most appropriate display because it uses separate bars to show how many observations fall into each category or discrete value. Here, the bar above 1 hour would have height 3, the bar above 2 hours would have height 6, the bar above 3 hours would have height 4, and the bar above 4 hours would have height 2. A line graph is inappropriate because the data are not measuring change over time. A pie chart could show proportions, but the question specifically asks for frequency of exercise hours, making a bar chart clearer and more direct. A scatterplot requires two quantitative variables and is used to study association, not a one-variable frequency distribution. References
/topics from the Study Guide: frequency distributions, bar charts, single-variable data displays, quantitative
/discrete data.
NEW QUESTION # 69
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