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| Section | Objectives |
|---|---|
| Probability | - Probability rules
|
| Probability Distributions | - Continuous distributions
|
| Statistical Inference | - Hypothesis testing
|
| Regression and Correlation | - Relationship analysis
|
| Descriptive Statistics | - Data summarization
|
>> Applied-Probability-and-Statistics Latest Dumps Questions <<
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NEW QUESTION # 69
Chi-square test used for:
Answer: A
Explanation:
A chi-square test is commonly used to analyze categorical data, especially to determine whether two categorical variables are associated. In a chi-square test of independence, data are arranged in a contingency table, and observed cell counts are compared with expected cell counts under the assumption that the variables are independent. If the observed counts differ substantially from the expected counts, there is evidence of association between the categorical variables. For example, a chi-square test could examine whether voting preference is associated with age group or whether product preference differs by region.
Option B describes comparing means, which is typically handled by a t-test or related procedure. Option C refers to regression, which models relationships between variables, often involving quantitative outcomes.
Option D refers to variance, which is tested using different procedures depending on context. The key phrase is "categorical variables": chi-square methods work with counts in categories. Study Guide references/topics:
categorical data, contingency tables, chi-square test, association.
NEW QUESTION # 70
A die is rolled twice. Probability of rolling two sixes?
Answer: C
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 # 71
Sum of probabilities in sample space = ?
Answer: B
Explanation:
The probabilities of all outcomes in a complete sample space must sum to 1. A sample space contains every possible outcome of a probability experiment, and one of those outcomes must occur. For example, when rolling a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, and 6. Each has probability 1/6, and the sum is 1/6 +
1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1. A total probability of 0 would mean no outcome can occur, which is impossible for a valid experiment. A total greater than 1 violates probability rules because probabilities cannot exceed certainty. "Cannot exceed 2" is too broad and mathematically invalid, since the exact total must equal
1. This principle is foundational for checking probability distributions and validating whether assigned probabilities are coherent. Study Guide references/topics: sample space, probability axioms, total probability, theoretical probability.
NEW QUESTION # 72
t-test used when:
Answer: D
Explanation:
A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.
NEW QUESTION # 73
Dataset: 3, 5, 7, 9, 11. Median = ?
Answer: A
Explanation:
The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.
NEW QUESTION # 74
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