An organization advocating for tax simplification has proposed the implementation of an alternative flat tax system to replace the existing Federal income tax.Featuring a very simple two-line tax form –How much money did you make?Send itIn an attempt to identify the partisan nature of support for their proposal, the tax reformers have conducted a simple survey. They collected random samples ofn1 = 120 Republican voters and n2 = 80 Democrat voters, polled the sampled respondents and noted for each group the number of voters who favor the flat tax proposal. The results of the survey are summarized in the table below.Political AffiliationFavor (X)Total (n)Proportion (X/n)Republican90120p-hat1 = 90/120 = 0.75Democrat5080p-hat2 = 50/80 = 0.625Total140200p-hat = 140/200 = 0.700Required Parts a. Initial concerns are for assessing the level of support among Democrats in particular, so for now we focus on the Democrat line (the second line) of the survey summary table. Develop a 95% confidence interval estimate for the proportion of Democrats who favor the flatb. Our flat tax heroes, concerned with the precision (or possible lack thereof) of the estimated proportion of Democrats in favor, are considering how a follow up study might estimate more precisely the proportion of Democrats in favor of the flat tax. How large a sample of Democrats should be selected to estimate the proportion in favor to within plus-or-minus 0.05 with 95% confidence? Note that the already existing study summarized above provides a source of planning information for the contemplated futurec. The bottom-line issue, with respect to Democratic support for the flat tax, is whether or not Democrats, as a group, favor the flat tax. Do the survey data provide sufficient evidence to conclude that the proportion of Democrats favoring the flat tax exceeds 5? Conduct your test at the α = 0.05 level of significance and report the p-value for your testd. Our tax reformers now turn to a comparative analysis of Republican versus Democratic support for the proposed flat tax. Estimate the difference [Republican - Democrat] between the proportions of individuals who favor the flat tax proposal and develop a 95% confidence interval for the estimated difference.e. Is there sufficient evidence, based upon the survey data, to conclude that the difference in proportions, [Republican - Democrat], that favor the proposed flat tax is significant (significantly different from zero?) Conduct your test at the α = 0.05 level of significance and report the p-value for your test. Be sure to identify the hypotheses to be tested and state your conclusion in managerial **Proportions Estimation and Testing Problem****Table 1a: Normal Curve Lower-Half Cumulative Areas**The table below presents the cumulative probabilities for a standard normal distribution, denoted as \( P(Z < z_0) \), where \( Z \) represents a standard normal random variable and \( z_0 \) is a specific value. This table is instrumental for statistical analysis involving z-scores, particularly in hypothesis testing and estimation.---**Table Description:**- **Columns:** Represent the hundredths place of the decimal value of \( z_0 \) (0.00 to 0.09).- **Rows:** Represent the integer and tenths place values of \( z_0 \) (ranging from -3.5 to 0.0).Values in the table provide the cumulative probability from the left of the curve up to \( z_0 \).---**Graph Description:**A diagram at the top illustrates a normal distribution curve, emphasizing the area to the left of a specific point \( z_0 \) on the horizontal axis. This shaded area corresponds to the cumulative probability values in the table.---**Table Example Entries:**- For \( z_0 = -2.3 \) with a hundredths place of 0.05, the cumulative probability is 0.01072.- For \( z_0 = -1.0 \), with a hundredths place of 0.04, the cumulative probability is 0.15151.- For \( z_0 = -0.3 \), with a hundredths place of 0.02, the cumulative probability is 0.38209.This table provides a crucial tool for those working with the standard normal distribution, allowing for the determination of probabilities and critical values essential in statistical procedures. Use this table to find the probability that a standard normal variable \( Z \) is less than a given value \( z_0 \). ## Proportions Estimation and Testing Problem### Table 1b: Normal Curve Upper-Half Cumulative Areas#### Diagram DescriptionThe diagram at the top of the table displays a standard normal distribution curve, also known as a bell curve. The curve is symmetrically centered around a vertical line labeled "z₀," which represents a specific point on the horizontal axis. The area under the curve to the left of z₀ is shaded in blue, highlighting the cumulative probability associated with that value of z.#### Table DescriptionThis table presents the cumulative probabilities for the standard normal distribution, representing Pr(Z < z₀). These probabilities are used to estimate the proportion of values that fall below a given z-score in a normal distribution.#### Table EntriesFor each z-score (z₀), the table provides cumulative probability values up to two decimal places.- The first column lists the main z-score (z₀) values from 0.0 to 3.6.- The top row displays decimal increments from 0.00 to 0.09 to give finer precision to each z-score.- The intersecting cell of a row and column gives the cumulative probability for that specific z-score.#### Example UsageTo find the cumulative probability for a z-score of 1.35:1. Locate 1.3 in the leftmost column.2. Move horizontally to the column labeled 0.05 in the top row.3. The intersection point gives the cumulative probability: 0.9115.This table is a critical tool in statistics for determining probabilities, making inferences about data, and hypothesis testing in normal distributions.

since multiple parts are given, first two parts answered in detail. Kindly repost for more help .

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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Required Parts

a. Initial concerns are for assessing the level of support among Democrats in particular, so for now we focus on the Democrat line (the second line) of the survey summary table. Develop a 95% confidence interval estimate for the proportion of Democrats who favor the flat

b. Our flat tax heroes, concerned with the precision (or possible lack thereof) of the estimated proportion of Democrats in favor, are considering how a follow up study might estimate more precisely the proportion of Democrats in favor of the flat tax. How large a sample of Democrats should be selected to estimate the proportion in favor to within plus-or-minus 0.05 with 95% confidence? Note that the already existing study summarized above provides a source of planning information for the contemplated future

c. The bottom-line issue, with respect to Democratic support for the flat tax, is whether or not Democrats, as a group, favor the flat tax. Do the survey data provide sufficient evidence to conclude that the proportion of Democrats favoring the flat tax exceeds 5? Conduct your test at the α = 0.05 level of significance and report the p-value for your test

d. Our tax reformers now turn to a comparative analysis of Republican versus Democratic support for the proposed flat tax. Estimate the difference [Republican - Democrat] between the proportions of individuals who favor the flat tax proposal and develop a 95% confidence interval for the estimated difference.

e. Is there sufficient evidence, based upon the survey data, to conclude that the difference in proportions, [Republican - Democrat], that favor the proposed flat tax is significant (significantly different from zero?) Conduct your test at the α = 0.05 level of significance and report the p-value for your test. Be sure to identify the hypotheses to be tested and state your conclusion in managerial

**Proportions Estimation and Testing Problem**

**Table 1a: Normal Curve Lower-Half Cumulative Areas**

The table below presents the cumulative probabilities for a standard normal distribution, denoted as \( P(Z < z_0) \), where \( Z \) represents a standard normal random variable and \( z_0 \) is a specific value. This table is instrumental for statistical analysis involving z-scores, particularly in hypothesis testing and estimation.

---

**Table Description:**

- **Columns:** Represent the hundredths place of the decimal value of \( z_0 \) (0.00 to 0.09).
- **Rows:** Represent the integer and tenths place values of \( z_0 \) (ranging from -3.5 to 0.0).

Values in the table provide the cumulative probability from the left of the curve up to \( z_0 \).

---

**Graph Description:**

A diagram at the top illustrates a normal distribution curve, emphasizing the area to the left of a specific point \( z_0 \) on the horizontal axis. This shaded area corresponds to the cumulative probability values in the table.

---

**Table Example Entries:**

- For \( z_0 = -2.3 \) with a hundredths place of 0.05, the cumulative probability is 0.01072.
- For \( z_0 = -1.0 \), with a hundredths place of 0.04, the cumulative probability is 0.15151.
- For \( z_0 = -0.3 \), with a hundredths place of 0.02, the cumulative probability is 0.38209.

This table provides a crucial tool for those working with the standard normal distribution, allowing for the determination of probabilities and critical values essential in statistical procedures. Use this table to find the probability that a standard normal variable \( Z \) is less than a given value \( z_0 \).

## Proportions Estimation and Testing Problem

### Table 1b: Normal Curve Upper-Half Cumulative Areas

#### Diagram Description

The diagram at the top of the table displays a standard normal distribution curve, also known as a bell curve. The curve is symmetrically centered around a vertical line labeled "z₀," which represents a specific point on the horizontal axis. The area under the curve to the left of z₀ is shaded in blue, highlighting the cumulative probability associated with that value of z.

#### Table Description

This table presents the cumulative probabilities for the standard normal distribution, representing Pr(Z < z₀). These probabilities are used to estimate the proportion of values that fall below a given z-score in a normal distribution.

#### Table Entries

For each z-score (z₀), the table provides cumulative probability values up to two decimal places.

- The first column lists the main z-score (z₀) values from 0.0 to 3.6.
- The top row displays decimal increments from 0.00 to 0.09 to give finer precision to each z-score.
- The intersecting cell of a row and column gives the cumulative probability for that specific z-score.

#### Example Usage

To find the cumulative probability for a z-score of 1.35:
1. Locate 1.3 in the leftmost column.
2. Move horizontally to the column labeled 0.05 in the top row.
3. The intersection point gives the cumulative probability: 0.9115.

This table is a critical tool in statistics for determining probabilities, making inferences about data, and hypothesis testing in normal distributions.

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Political Affiliation	Favor (X)	Total (n)	Proportion (X/n)
Republican	90	120	p-hat1 = 90/120 = 0.75
Democrat	50	80	p-hat2 = 50/80 = 0.625
Total	140	200	p-hat = 140/200 = 0.700