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| Section | Objectives |
|---|---|
| Topic 1: Probability Distributions | - Discrete distributions
|
| Topic 2: Probability | - Probability rules
|
| Topic 3: Statistical Inference | - Estimation
|
| Topic 4: Descriptive Statistics | - Data summarization
|
| Topic 5: Regression and Correlation | - Relationship analysis
|
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NEW QUESTION # 122
Mean = 100, SD = 15, z = 2. Value = ?
Answer: C
Explanation:
A z-score expresses how many standard deviations a value lies above or below the mean. The formula is z = (x # #)/#. To solve for the raw value x, rearrange the formula: x = # + z#. Here, the mean # is 100, the standard deviation # is 15, and z = 2. Substitute these values: x = 100 + 2(15) = 100 + 30 = 130. Therefore, the raw value is 130. This means the value is two standard deviations above the mean. Option B, 115, would correspond to z = 1. Option C, 125, is not exactly two standard deviations above 100 when # = 15. Option D,
110, is less than one standard deviation above the mean. The correct value must add two full standard deviations to the mean. Study Guide references/topics: z-scores, standardization, normal distribution, raw score conversion.
NEW QUESTION # 123
Type II error # is:
Answer: D
Explanation:
A Type II error occurs when the null hypothesis is false but the test fails to reject it. Many introductory answer choices phrase this as "accept H# when false," though the more technically careful wording is "fail to reject H# when false." This is a false negative: the real effect or difference exists, but the test does not detect sufficient evidence. The probability of a Type II error is denoted #. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is incorrect because 1 # # is not #; # is the Type I error probability, while 1 # # is statistical power. Option D is too vague and does not identify a formal hypothesis- testing error. The defining condition for Type II error is missing a real effect by failing to reject a false null hypothesis. Study Guide references/topics: Type II error, beta, hypothesis testing, statistical power.
NEW QUESTION # 124
Best chart for categorical data?
Answer: C
Explanation:
A bar chart is the best display for categorical data because it shows the frequency or relative frequency of each category using separate bars. Categorical variables classify observations into groups, such as favorite color, type of transportation, political affiliation, or product category. A bar chart allows the viewer to compare category counts directly by bar height. A histogram is not appropriate because it is used for quantitative data grouped into numerical intervals. A scatterplot is used to examine the relationship between two quantitative variables, such as height and weight. A boxplot summarizes a quantitative distribution using quartiles, median, spread, and outliers. Since the question asks specifically about categorical data, the display must preserve category labels rather than numerical intervals or continuous measurement. Therefore, the bar chart is the correct choice. Study Guide references/topics: categorical data, bar charts, frequency displays, descriptive statistics.
NEW QUESTION # 125
Mean of Poisson # = 5 = ?
Answer: A
Explanation:
For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.
NEW QUESTION # 126
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 # 127
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