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| Section | Objectives |
|---|---|
| Statistical Inference | - Estimation and Confidence Intervals
|
| Probability Theory | - Probability Distributions
|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Regression and Modeling | - Linear Relationships
|
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NEW QUESTION # 142
Z-test used when:
Answer: D
Explanation:
A z-test for a population mean is used when the population standard deviation # is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic # hypothesized parameter) divided by the standard error. Knowing # allows the standard error to be computed using #/#n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when # is unknown. Option D is unrelated to the classic z- test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.
NEW QUESTION # 143
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: C
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 # 144
Sample mean = 40, SD = 8, n = 16. Standard error = ?
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. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.
NEW QUESTION # 145
Type II error # is:
Answer: A
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 # 146
There are 20 men in a room whose heights are reflected in inches as 68, 70, 73, 67, 71, 68, 76, 70, 73, 66, 68,
69, 71, 74, 73, 72, 65, 60, 70, and 78 inches respectively.
What is the median of these data?
Answer: A
Explanation:
The median is the middle value of an ordered data set. Because there are 20 observations, the number of data values is even, so the median is the average of the 10th and 11th values after the data are arranged from least to greatest. Ordering the heights gives 60, 65, 66, 67, 68, 68, 68, 69, 70, 70, 70, 71, 71, 72, 73, 73, 73, 74, 76,
78. The 10th value is 70, and the 11th value is also 70. The median is therefore (70 + 70) ÷ 2 = 70. This value divides the ordered heights into two equal halves: ten values are at or below 70, and ten values are at or above
70. The median is resistant to extreme values, so the low value 60 and the high value 78 do not distort it the way they could affect the mean. References/topics from the Study Guide: median, ordered data, measures of center, quantitative data.
NEW QUESTION # 147
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