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| Section | Objectives |
|---|---|
| Topic 1: Probability Theory | - Probability Distributions
|
| Topic 2: Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Topic 3: Regression and Modeling | - Linear Relationships
|
| Topic 4: Descriptive Statistics | - Two Variable Data Analysis
|
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NEW QUESTION # 54
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 # 55
A cafe recorded the total ice cream sales and the average maximum temperature of the day. The scatterplot shows the recorded data. The regression equation y = 13x # 598 estimates the total ice cream sales, y, of a day and the average maximum temperature, x, on that day.
What does the slope represent in this context?
Answer: A
Explanation:
In a linear regression equation of the form y = mx + b, the slope m gives the predicted change in the response variable y for a one-unit increase in the explanatory variable x. Here, y represents total ice cream sales and x represents average maximum temperature. The equation y = 13x # 598 has slope 13, so the model predicts that ice cream sales increase by about $13 for every 1°F increase in temperature. This is not the sales value at
0°F; that would be the intercept, #598, which is generally not meaningful in this practical context. It is also not the predicted sales at 100°F, because that would require substituting x = 100 into the regression equation.
The positive slope matches the upward trend in the scatterplot: higher temperatures are associated with higher ice cream sales. References/topics from the Study Guide: correlation and regression, slope interpretation, explanatory and response variables.
NEW QUESTION # 56
Standard error decreases when:
Answer: D
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.
NEW QUESTION # 57
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: D
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 # 58
Standard error decreases when:
Answer: C
Explanation:
The standard error of the mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Because n appears in the denominator under a square root, increasing the sample size decreases the standard error when the standard deviation is held constant. This reflects a central idea in sampling: larger samples tend to produce more stable and precise estimates of the population mean. Option C is incorrect because increasing the standard deviation increases the standard error, not decreases it. Option B is incomplete and does not identify what is decreasing. Option D is not the direct driver of standard error; confidence level affects the critical value and margin of error, but the standard error itself is determined by variability and sample size. The correct relationship is inverse: as sample size increases, standard error decreases. Study Guide references/topics: standard error, sample size, sampling variability, precision of estimates.
NEW QUESTION # 59
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