**Probability and Sampling in Healthcare Studies**According to *Reader's Digest*, 30% of primary care doctors believe their patients receive unnecessary medical care. The analysis below uses the z-table to answer related statistical inquiries.### TaskSuppose a sample of 400 primary care doctors is taken to analyze the proportion of doctors who think their patients receive unnecessary medical care.1. **Expected Value and Standard Error** - Calculate the expected sample proportion \( E(\hat{p}) \). - Determine the standard error \( \sigma_{\hat{p}} \). Fill in: - \( E(\hat{p}) = \_\_\_ \) (to 2 decimals) - \( \sigma_{\hat{p}} = \_\_\_ \) (to 4 decimals)2. **Probability Within Tolerance** - **b.** What is the probability that the sample proportion is within \(\pm 0.03\) of the population proportion? Round your answer to four decimals.3. **Probability with Larger Tolerance** - **c.** What is the probability that the sample proportion is within \(\pm 0.05\) of the population proportion? Round your answer to four decimals.4. **Effect of a Larger Sample** - **d.** Discuss the effect of increasing the sample size on the probabilities in parts (b) and (c). The probabilities would: [Select your answer]. Explain why: Increasing the sample size decreases the standard error, \( \sigma_{\hat{p}} \). [Select your answer].---This exercise facilitates a deeper understanding of how sample size affects precision and the probability of achieving results within a specified tolerance of the population proportion in statistical studies.

As per our guidelines, we are allowed to answer first three sub-parts only . Thanks Given : p = 0.3…

Answered: According to Reader's Digest, 30% of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Save Suppose a random sample of n = 390 teenagers 13 to 17 years of age was asked if they use social media. Of those surveyed, 276 stated that they do use social media. Find the sample proportion of teenagers 13 to 17 years of age who use social media. The sample proportion is p= (Round to three decimal places as needed.)

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