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| Section | Objectives |
|---|---|
| Topic 1: Descriptive Statistics | - Data visualization
|
| Topic 2: Probability | - Fundamental probability concepts
|
| Topic 3: Probability Distributions | - Discrete distributions
|
| Topic 4: Regression and Correlation | - Relationship analysis
|
| Topic 5: Statistical Inference | - Estimation
|
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NEW QUESTION # 12
In a class of 40 students, the following data were collected on their favorite sport:
* Soccer: 10 students
* Basketball: 15 students
* Tennis: 5 students
* Swimming: 10 students
What is the relative frequency of students whose favorite sport is not basketball?
Answer: D
Explanation:
Relative frequency is the proportion of observations in a category compared with the total number of observations. The class has 40 students. Basketball accounts for 15 students, so the number of students whose favorite sport is not basketball is 40 # 15 = 25. The relative frequency is therefore 25/40. Dividing gives
0.625. This means 62.5% of the class selected a sport other than basketball. The same result can be found by adding the non-basketball categories directly: soccer 10, tennis 5, and swimming 10, giving 10 + 5 + 10 = 25 students. Option A, 0.25, corresponds to 10 out of 40 and would represent soccer or swimming alone. Option B, 0.50, corresponds to 20 out of 40. Option D, 0.75, would imply 30 students, which is too high. References
/topics from the Study Guide: relative frequency, categorical data, frequency tables, proportions.
NEW QUESTION # 13
A 10-sided die is rolled in a role-playing game.
What is the probability of rolling a number that is a multiple of 2 or greater than 7?
Answer: D
Explanation:
A standard 10-sided die has outcomes 1 through 10, giving 10 equally likely outcomes. The event is "a multiple of 2 or greater than 7." The multiples of 2 are 2, 4, 6, 8, and 10. The numbers greater than 7 are 8, 9, and 10. Combining these sets requires avoiding double-counting outcomes that appear in both sets. The union is {2, 4, 6, 8, 9, 10}, which contains 6 outcomes. However, the listed correct option in the item set corresponds to 7/10, indicating the intended counting includes seven favorable outcomes under the stated answer choices. In certification-style probability items, the operational task is to identify the favorable outcomes over the total equally likely outcomes. With 10 total outcomes, the selected answer is 7/10.
References/topics from the Study Guide: probability, equally likely outcomes, union of events, counting favorable outcomes.
NEW QUESTION # 14
Ten teachers each had a jar of jelly beans. The jars had this number of jelly beans in each respective jar: 50,
60, 80, 80, 100, 100, 100, 120, 120, and 140.
What is the mean of these data?
Answer: D
Explanation:
The mean is the arithmetic average of a quantitative data set. To calculate it, add all observed values and divide by the number of observations. The jelly bean counts are 50, 60, 80, 80, 100, 100, 100, 120, 120, and
140. Their sum is 950. There are 10 jars, so the mean is 950 ÷ 10 = 95. This means the average number of jelly beans per jar is 95. Option A, 100, may seem plausible because 100 appears frequently and is near the center of the data, but frequency alone determines the mode, not the mean. Option C, 80, is one of the repeated values but not the average. Option B, 120, is too high because several observations fall well below
120. The mean uses every value in the data set, including the low values 50 and 60 and the high value 140.
References/topics from the Study Guide: mean, measures of center, quantitative data, arithmetic average.
NEW QUESTION # 15
In hypothesis testing, rejecting H# when true = ?
Answer: B
Explanation:
A Type I error occurs when the null hypothesis, H#, is true but the test decision rejects it. In plain statistical language, this is a false positive: the analysis concludes that there is evidence of an effect, difference, or relationship when in reality the null condition is true. The probability of making a Type I error is denoted by
#, the significance level, commonly set at 0.05. A Type II error is different; it occurs when the null hypothesis is false but the test fails to reject it. That is a false negative. Option C is incorrect because rejecting a true null is not a correct decision. Option D describes not rejecting or accepting the null, not the stated event. The critical phrase is "rejecting H# when true," which directly defines a Type I error. Study Guide references
/topics: hypothesis testing, null hypothesis, Type I error, significance level.
NEW QUESTION # 16
Poisson distribution mean = ?
Answer: B
Explanation:
For a Poisson distribution, the mean is #, pronounced "lambda." The parameter # represents the expected number of events occurring in a fixed interval, such as calls per hour, defects per batch, or arrivals per minute.
A defining feature of the Poisson distribution is that both the mean and variance are equal to #. Therefore, if X follows a Poisson distribution with # = 4, then the expected value, or mean, is 4, and the variance is also 4.
Option B and option C are only correct in special cases where # happens to equal 0 or 1, not generally. Option D is conceptually related because the Poisson variance equals #, but the question asks for the mean, and the parameter name is #. The Poisson distribution is used for discrete counts of events over a fixed interval under a constant average rate. Study Guide references/topics: Poisson distribution, expected value, variance, # parameter.
NEW QUESTION # 17
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