need help with the two red x parts ### Understanding Sampling DistributionsIn a study published in *Reader's Digest* (March 2009), it was found that people tend to discard 12% of the groceries they purchase. Assuming this percentage represents the true population proportion, we aim to conduct a sample survey of 540 grocery shoppers to explore this behavior further. **a. Sampling Distribution**To represent the sampling distribution of $\bar{p}$, the proportion of groceries discarded by the surveyed sample, follow these steps:1. **Assumptions**: We can assume the sampling distribution to be normally distributed if $ np \geq 5 $ and $ n(1-p) \geq 5 $. 2. **Proportion (p)**: Given as 0.12.3. **Standard Error**: Calculate using the formula: \[ \sigma(\bar{p}) = \sqrt{\frac{p(1-p)}{n}} \] where $\sigma(\bar{p})$ is the standard error of the proportion and $n$ is the sample size.**b. Probability Calculation for ±0.03**Determine the probability that this survey will yield a sample proportion within ±0.03 of the true population proportion. Fill in the probability in four decimal places after calculation.**c. Probability Calculation for ±0.015**Calculate the probability that the survey will yield a sample proportion within ±0.015 of the population proportion:- The probability is given as 0.7154.Through understanding and calculating these values, researchers can estimate the accuracy and reliability of their findings regarding the proportion of groceries discarded by consumers.

Given information- Sample size, n = 540 Population proportion, p = 0.12

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table. a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals). Can assume to be normally distributed because np>=5 and n(1-p)>=5 p = .12 standard error of the proportion o( p ) = b. What is the probability that your survey will provide a sample proportion within +.03 of the population proportion (to 4 decimals)?

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. Use z-table. a. Show the sampling distribution of (P), the proportion of groceries thrown out by your sample respondents (to 4 decimals). Can assume to be normally distributed because np>=5 and n(1-p)>=5 p = .12 standard error of the proportion o( p ) = b. What is the probability that your survey will provide a sample proportion within +.03 of the population proportion (to 4 decimals)?

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

need help with the two red x parts

### Understanding Sampling Distributions

In a study published in *Reader's Digest* (March 2009), it was found that people tend to discard 12% of the groceries they purchase. Assuming this percentage represents the true population proportion, we aim to conduct a sample survey of 540 grocery shoppers to explore this behavior further.

**a. Sampling Distribution**

To represent the sampling distribution of $\bar{p}$, the proportion of groceries discarded by the surveyed sample, follow these steps:

1. **Assumptions**: We can assume the sampling distribution to be normally distributed if $ np \geq 5 $ and $ n(1-p) \geq 5 $.

2. **Proportion (p)**: Given as 0.12.

3. **Standard Error**: Calculate using the formula:
\[
\sigma(\bar{p}) = \sqrt{\frac{p(1-p)}{n}}
\]
where $\sigma(\bar{p})$ is the standard error of the proportion and $n$ is the sample size.

**b. Probability Calculation for ±0.03**

Determine the probability that this survey will yield a sample proportion within ±0.03 of the true population proportion. Fill in the probability in four decimal places after calculation.

**c. Probability Calculation for ±0.015**

Calculate the probability that the survey will yield a sample proportion within ±0.015 of the population proportion:

- The probability is given as 0.7154.

Through understanding and calculating these values, researchers can estimate the accuracy and reliability of their findings regarding the proportion of groceries discarded by consumers.

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