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| Section | Objectives |
|---|---|
| Probability Distributions | - Continuous distributions
|
| Probability | - Probability rules
|
| Regression and Correlation | - Relationship analysis
|
| Descriptive Statistics | - Data summarization
|
| Statistical Inference | - Hypothesis testing
|
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NEW QUESTION # 132
Determine z in the equation:
1/(6z) = 2/9
Answer: A
Explanation:
The equation 1/(6z) = 2/9 is a proportion because it sets two fractions equal to each other. To solve it, use cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction: 1 × 9 = 2 × 6z. This gives 9 = 12z. To isolate z, divide both sides by 12: z = 9/12. This fraction can also be simplified to 3/4, but the answer choices list the unsimplified equivalent form 9/12. The other options do not satisfy the original equation. For example, if z = 2/54, then 6z is very small and the left side becomes much larger than 2/9. If z =
12/9 or 18/2, the denominator becomes too large, making the left side too small. References/topics from the Study Guide: proportions, solving equations, cross multiplication, equivalent fractions.
NEW QUESTION # 133
Sample mean = 40, SD = 8, n = 16. Standard error = ?
Answer: B
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 # 134
Which distribution models number of successes in fixed independent trials?
Answer: C
Explanation:
The binomial distribution models the number of successes in a fixed number of independent trials when each trial has only two possible outcomes, usually labeled success and failure, and the probability of success remains constant from trial to trial. These four conditions define the binomial setting: fixed number of trials, independent trials, two outcomes per trial, and constant success probability. Examples include the number of heads in 10 coin flips, the number of defective items in a sample when the defect probability is constant, or the number of students who pass an exam out of a fixed group. The normal distribution describes continuous bell-shaped data, not counts of successes. The Poisson distribution models counts of events occurring over a fixed interval when events occur at a constant average rate. The uniform distribution assigns equal probability across outcomes or intervals. Because the question explicitly states "number of successes" and "fixed independent trials," the correct model is binomial. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete random variables.
NEW QUESTION # 135
Null hypothesis for a new drug shows no effect. True statement?
Answer: C
Explanation:
The null hypothesis represents the default claim or baseline assumption in hypothesis testing. For a new drug, a typical null hypothesis states that the drug has no effect, no difference from placebo, or no improvement over the existing standard. The testing process begins by assuming the null hypothesis is true, then evaluates whether the sample evidence is strong enough to reject it. Therefore, the correct statement is that researchers assume no effect until evidence suggests otherwise. This does not mean the drug is proven ineffective; it means the burden of evidence lies with demonstrating an effect. Option B is the alternative hypothesis, not the null. Option C overstates the conclusion because failing to reject the null does not prove the drug has no effect. Option D is false because this type of claim is testable using experimental data and statistical inference.
Study Guide references/topics: null hypothesis, alternative hypothesis, hypothesis testing, statistical evidence.
NEW QUESTION # 136
Review the following inequality:
y # #4x + 1
Which shaded region is described by this inequality?
Answer: C
Explanation:
The inequality y # #4x + 1 has boundary line y = #4x + 1. The slope is #4, so the line must decrease steeply from left to right. The y-intercept is 1, so the line must cross the vertical axis at y = 1. Because the inequality uses "#," the boundary line must be solid, meaning points on the line are included in the solution set. The solution region must be below the line because y is less than or equal to the expression #4x + 1. A quick test point confirms this. Substitute (0, 0): 0 # #4(0) + 1, giving 0 # 1, which is true. Therefore, the shaded solution region must include the origin. Graph D shows a solid, steep downward-sloping line crossing the y-axis near 1 and shades the region containing the origin and below the boundary. References/topics from the Study Guide:
linear inequalities, slope-intercept form, boundary lines, test-point method.
NEW QUESTION # 137
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