University:
Washington State University
Course:
MATH 172 | Calculus II
Academic year:

2024
Views:

330

Pages:

3
Author:

Bailey Ayala

Question 1 True Statement About the Sampling Distribution of Means: Answer: C. Sampling distributions of means get closer to normality as the sample size increases. Question 2 Explain Why the Central Limit Theorem Applies to Sample Means but Not Always to Other Statistics: Answer: The Central Limit Theorem (CLT) applies only to the sample mean because it specifically states that the distribution of the sample mean approaches a normal distribution as the sample size increases. For other statistics, such as sample medians or variances, the CLT does not always hold unless specific conditions are met. Question 3 Describe Sampling Distributions and Sampling Variability: Sampling distributions represent the probability distribution of all possible values for a statistic (e.g., mean) computed from a sample. Sampling variability measures the variability in a statistic across multiple samples due to chance differences. Explain the Central Limit Theorem: The CLT states that the distribution of the sample mean approaches normality as the sample size increases, regardless of the shape of the population distribution. How Confidence Intervals Are Created: Confidence intervals are created using the formula: 𝐶 𝐼 = 𝑥 ˉ ± 𝑍 ⋅ 𝜎 𝑛 CI= x ˉ ±Z⋅ n σ 𝑥 ˉ x ˉ : Sample mean 𝑍 Z: Critical value 𝜎 σ: Population standard deviation 𝑛 n: Sample size These intervals indicate the range in which the true population parameter is likely to lie with a certain confidence level (e.g., 95%).