Math Problem Statement

A company surveys employees. The company is too large to check each response, so samples of 50 are taken, and the tendency is that three-fourths of the employees are happy. For the mean of the sample distribution of sample proportions, answer the following questions. A) How does this affect the mean? B) How does this affect the standard Deviation? C) How does this affect the variance?

Solution

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Math Problem Analysis

Mathematical Concepts

Sampling Distribution
Proportion
Standard Deviation
Variance

Formulas

Mean of the sampling distribution: μ̂p = p
Standard deviation of the sample proportion: σ̂p = √[p(1 − p)/n]
Variance of the sample proportion: Variance = σ̂p^2

Theorems

Central Limit Theorem

Suitable Grade Level

College Level (Statistics)