The problem presented explores the concept of sampling distributions related to the mean annual rainfall in the states of California and New York.**Context**: - California's mean annual rainfall: 22 inches- New York's mean annual rainfall: 42 inches- Standard deviation for both states: 3 inches- Sample size for California: 30 years- Sample size for New York: 45 years**Tasks**:(a) **Calculate the Sampling Distribution for California**:- $ E(\bar{x}) $: Expected mean annual rainfall for California's sample- $ \sigma_{\bar{x}} $: Standard error of the mean for California's sample(b) **Calculate the Sampling Distribution for New York**:- $ E(\bar{x}) $: Expected mean annual rainfall for New York's sample- $ \sigma_{\bar{x}} $: Standard error of the mean for New York's sample(c) **Compare the Standard Errors**:- Determine in which case (California or New York) the standard error of $ \bar{x} $ is smaller and explain why. Focus is given to the relationship between sample size and the standard error: $ \sigma_{\bar{x}} = \sigma / \sqrt{n} $.**Educational Focus**:This problem is an application of statistical concepts, particularly focusing on sampling distributions, expected values, and standard errors. It highlights how these parameters are affected by different sample sizes and how they relate to the variability in estimated sample means.

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places. (a) Show the samplinn distribution

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places. (a) Show the samplinn distribution

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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