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| Section | Objectives |
|---|---|
| Topic 1: Probability | - Probability rules
|
| Topic 2: Probability Distributions | - Continuous distributions
|
| Topic 3: Regression and Correlation | - Relationship analysis
|
| Topic 4: Statistical Inference | - Estimation
|
| Topic 5: Descriptive Statistics | - Data visualization
|
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NEW QUESTION # 94
Correlation r = 0.8 # strong positive relationship #
Answer: B
Explanation:
A correlation coefficient of r = 0.8 indicates a strong positive linear relationship between two quantitative variables. The positive sign means that as one variable increases, the other tends to increase. The magnitude,
0.8, is close to 1, which indicates a strong linear pattern. It is not perfect, because perfect positive correlation would be r = 1, but it is clearly stronger than a weak or moderate association. Option B is incorrect because the interpretation matches both the sign and magnitude of r. Option C is incorrect because correlation is used for quantitative variables, not categorical variables. Option D is incorrect because a negative r would indicate a negative relationship. Importantly, correlation does not prove causation; it describes the direction and strength of linear association. Study Guide references/topics: correlation coefficient, positive association, linear relationship, scatterplot interpretation.
NEW QUESTION # 95
A researcher has collected information on students from a school. The researcher wants to display the ethnic groups represented in the school.
Which pair of graphs both display data in this manner?
Answer: D
Explanation:
Ethnic group is a categorical variable because it classifies students into named groups rather than measuring a numerical quantity. Categorical data are commonly displayed with bar graphs or pie charts. A bar graph shows the frequency or relative frequency of each category using separate bars, making it easy to compare group sizes. A pie chart shows how the whole student population is divided among categories, making it useful for displaying proportions or percentages. Therefore, the correct pair is bar graph and pie chart. A box plot is used for quantitative data and summarizes values using quartiles and a median, so it is not appropriate for ethnic categories. A line graph is typically used to show change over time or ordered numerical trends. A histogram is used for distributions of quantitative data grouped into intervals, not named categories. Since the goal is to display category membership, both selected graphs must support categorical frequency or percentage displays. References/topics from the Study Guide: categorical data displays, bar graphs, pie charts, relative frequency.
NEW QUESTION # 96
A die is rolled twice. Probability of rolling two sixes?
Answer: D
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 # 97
One-sample t-test compares:
Answer: A
Explanation:
A one-sample t-test is used to compare a sample mean to a hypothesized or known population mean when the population standard deviation is unknown and the data are approximately normal or the sample size is sufficiently large. The test statistic evaluates how far the sample mean is from the hypothesized mean in standard error units. Option A is therefore correct. A two-sample t-test compares means from two independent groups, so option B describes a different test. Tests of variances use procedures such as chi-square or F-based methods depending on context, so option C is not appropriate. Tests of proportions use z procedures for categorical success/failure data, not a one-sample t-test for means. The t-test is part of inferential statistics because it uses sample evidence to make a decision about a population parameter. Study Guide references
/topics: one-sample t-test, sample mean, population mean, hypothesis testing.
NEW QUESTION # 98
A university surveys faculty and students to determine support for a new campus recycling initiative.
The results of the survey are shown in the following 2 × 2 contingency table:
Which statement is true?
Answer: D
Explanation:
This problem compares conditional percentages across two groups. For faculty members, 40 out of 50 support the recycling initiative, so the faculty support rate is 40/50 = 0.80, or 80%. For students, 200 out of 500 support the initiative, so the student support rate is 200/500 = 0.40, or 40%. Comparing 80% and 40% shows that faculty members are twice as likely as students to support the initiative. This is not a slight difference; it is a large difference of 40 percentage points. Therefore, the correct statement is that faculty members are much more likely than students to support the recycling initiative. The table contains two categorical variables: group type and recycling opinion. Conditional percentages are the appropriate numerical tool because the goal is to compare support within each group. References/topics from the Study Guide:
contingency tables, two-way categorical data, conditional percentages, comparative proportions.
NEW QUESTION # 99
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