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| Section | Objectives |
|---|---|
| Topic 1: Descriptive Statistics | - Two Variable Data Analysis
|
| Topic 2: Statistical Inference | - Estimation and Confidence Intervals
|
| Topic 3: Regression and Modeling | - Linear Relationships
|
| Topic 4: Probability Theory | - Fundamental Probability Concepts
|
>> Applied-Probability-and-Statistics Lab Questions <<
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NEW QUESTION # 91
Which graph displays data in a manner that is accurate?
Answer: C
Explanation:
The accurate display is the bar graph labeled "Number of Feet Traveled" with the vertical axis showing the number of feet and the horizontal axis identifying the student travelers. For discrete observations associated with individual students, a bar graph is appropriate because each bar represents a separate category or individual and its height represents the measured value. Option A is inaccurate because its title states
"Number of Miles Traveled," while the vertical axis is labeled in feet; this creates a unit mismatch. Option C uses a pie chart, which is designed to show parts of a whole, not individual measured distances unless the goal is proportional composition. Option D uses a line graph, which is typically reserved for ordered change, especially over time; connecting student traveler values implies continuity or trend that is not justified. The correct graph must use consistent units, clear labels, and an appropriate display type. References/topics from the Study Guide: data displays, bar graphs, categorical identifiers, quantitative measurements, graph accuracy.
NEW QUESTION # 92
Determine x:
4 + x = 6 # x
Answer: D
Explanation:
The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
1, which is not valid. The correct solution is the value that balances both sides of the equation. References
/topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.
NEW QUESTION # 93
Probability it does NOT rain = 1 # 0.25 = ?
Answer: C
Explanation:
This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
# P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.
NEW QUESTION # 94
A city council surveys residents and business owners about a proposed new public transportation system. The results of the survey are shown in the following 2 × 2 contingency table.
Which statement is true?
Answer: C
Explanation:
This question requires comparing conditional percentages from a two-way table. For residents, 150 out of 200 are in favor of the proposed transportation system. The resident support rate is therefore 150/200 = 0.75, or
75%. For business owners, 30 out of 100 are in favor. The business owner support rate is 30/100 = 0.30, or
30%. The difference is 75% # 30% = 45 percentage points, which is a large gap. Therefore, a resident is much more likely than a business owner to favor the new transportation system. Option A understates the magnitude of the difference by calling it slight. Options B and C reverse the direction of the comparison because residents have the higher support rate, not the lower one. The appropriate statistical tool here is conditional percentage because support is being compared within each respondent group. References/topics from the Study Guide: contingency tables, conditional percentages, two-variable categorical data, comparative proportions.
NEW QUESTION # 95
In hypothesis testing, rejecting H# when true = ?
Answer: C
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 # 96
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