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| Section | Objectives |
|---|---|
| Probability Theory | - Probability Distributions
|
| Regression and Modeling | - Linear Relationships
|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Descriptive Statistics | - Single Variable Data Analysis
|
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NEW QUESTION # 17
A biologist is studying the relationship between plant species, species A, species B, and species C, and the average height of the plants.
How should this study be classified?
Answer: C
Explanation:
This study compares two variables: plant species and average plant height. Plant species is categorical because it places each plant into a named group, such as species A, species B, or species C. These categories are labels rather than numerical measurements. Average height, however, is quantitative because it is measured numerically and can be compared using arithmetic operations such as differences, averages, and ranges. Since the explanatory or grouping variable is categorical and the measured outcome is quantitative, the relationship is classified as categorical-to-quantitative. This classification determines which statistical tools are appropriate. For example, side-by-side box plots, group means, or comparative summaries would be suitable because they compare numerical measurements across categories. A categorical-to-categorical study would involve two label-based variables, such as species and color group. A quantitative-to-quantitative study would involve two numerical variables, such as height and growth rate. References/topics from the Study Guide: two-variable data, categorical variables, quantitative variables, comparative statistical summaries.
NEW QUESTION # 18
Type I error # = 0.05 means:
Answer: C
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 # 19
A die is rolled twice. Probability of rolling two sixes?
Answer: B
Explanation:
Rolling a standard six-sided die twice creates two independent events. The probability of rolling a six on the first roll is 1/6 because there is one favorable outcome, six, out of six equally likely outcomes. The probability of rolling a six on the second roll is also 1/6. Because the outcome of the first roll does not affect the outcome of the second roll, the multiplication rule for independent events applies. Thus, P(six and six) = 1/6 × 1/6 = 1
/36. Another way to verify the result is to list the sample space: two die rolls produce 6 × 6 = 36 equally likely ordered outcomes. Only one outcome, (6, 6), satisfies the condition of two sixes. Therefore, the probability is
1 favorable outcome out of 36 total outcomes. Study Guide references/topics: independent events, multiplication rule, sample space, theoretical probability.
NEW QUESTION # 20
Type II error occurs when:
Answer: B
Explanation:
A Type II error occurs when the null hypothesis is false but the statistical test fails to reject it. In many answer choices, this is expressed as "accepting the null when false," though the more precise language is "failing to reject the null." This error is a false negative: the test misses a real effect, difference, or relationship. For example, if a medication truly improves recovery but a study fails to detect sufficient evidence of improvement, that is a Type II error. Option B describes a Type I error, which occurs when a true null hypothesis is rejected. Option C is not an error. Option D is too vague; statistical decision errors refer specifically to incorrect conclusions about hypotheses, not ordinary data-entry mistakes. The probability of a Type II error is denoted #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.
NEW QUESTION # 21
There are 12 cell phone charging cords available at a store for purchase. The length of each charging cord in inches is reflected as 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12, respectively.
What are the mean of these data?
Answer: B
Explanation:
The mean is the arithmetic average of a data set. To find it, add all values and divide by the number of values.
The cord lengths are 3, 3, 4, 6, 6, 6, 6, 7, 10, 10, 11, and 12. Their sum is 84. Since there are 12 charging cords, divide 84 by 12 to obtain 7. Therefore, the mean cord length is 7 inches. This value represents the balance point of the distribution, not necessarily a value that must occur most often. In this data set, 6 appears most frequently, so 6 is the mode, but the question asks for the mean. Option B, 8, and option C, 9, are too large because several values are below 7. Option D, 6, identifies the most common value rather than the average. References/topics from the Study Guide: mean, measures of center, quantitative data, arithmetic average.
NEW QUESTION # 22
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