Z= and P-value= ### Hypothesis Testing for College Affordability**Scenario:** Among a simple random sample of 328 American adults who do not have a four-year college degree and are not currently enrolled in school, 49% said they decided not to go to college because they could not afford school.**Problem Statement:**(a) A newspaper article states that only a minority of Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement. (Use a significance level of 0.05.)#### Steps to Conduct Hypothesis Testing:**1. State the Appropriate Null and Alternative Hypotheses**From the provided options, the correct hypotheses are:- Null Hypothesis (H₀): $ p = 0.5 $- Alternative Hypothesis (H₁): $ p < 0.5 $Only one option is correct:```H₀: p = 0.5H₁: p < 0.5```The choice is marked as correct with a green check.**2. Check the Relevant Conditions**- **Random Sample:** The sample is random.- **Sample Representation:** The sample represents less than 10% of all Americans.- **Independence:** Whether or not one person in the sample decided not to go to college because they can't afford it is independent of another.- **Success-Failure Condition:** The success-failure condition is met since the number of successes and failures is greater than 10.All the conditions are checked and marked with green check marks to indicate they are satisfied.**3. Calculate the Test Statistic and Determine the p-value**To complete the hypothesis testing, calculate:- The test statistic $ z $- The p-valueBoxes are provided for these values but are currently empty:```z = ____p-value = ____```It is important to round the test statistic to two decimal places and the p-value to four decimal places as instructed.**Summary**This procedure sets up the hypothesis test for determining whether the statement that a minority of Americans decide not to go to college due to financial reasons is supported by the sample data. All relevant conditions are met, ensuring the validity of the test. To reach a conclusion, the test statistic and p-value must be calculated and compared against the significance level.This

The hypothesized proportion is 0.5.

Answered: Calculate the test statistic and…

Calculate the test statistic and determine the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) p-value =

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

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.

Question

Z= and P-value=

### Hypothesis Testing for College Affordability

**Scenario:**
Among a simple random sample of 328 American adults who do not have a four-year college degree and are not currently enrolled in school, 49% said they decided not to go to college because they could not afford school.

**Problem Statement:**
(a) A newspaper article states that only a minority of Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement. (Use a significance level of 0.05.)

#### Steps to Conduct Hypothesis Testing:

**1. State the Appropriate Null and Alternative Hypotheses**

From the provided options, the correct hypotheses are:

- Null Hypothesis (H₀): $ p = 0.5 $
- Alternative Hypothesis (H₁): $ p < 0.5 $

Only one option is correct:
```
H₀: p = 0.5
H₁: p < 0.5
```
The choice is marked as correct with a green check.

**2. Check the Relevant Conditions**

- **Random Sample:** The sample is random.
- **Sample Representation:** The sample represents less than 10% of all Americans.
- **Independence:** Whether or not one person in the sample decided not to go to college because they can't afford it is independent of another.
- **Success-Failure Condition:** The success-failure condition is met since the number of successes and failures is greater than 10.

All the conditions are checked and marked with green check marks to indicate they are satisfied.

**3. Calculate the Test Statistic and Determine the p-value**

To complete the hypothesis testing, calculate:

- The test statistic $ z $
- The p-value

Boxes are provided for these values but are currently empty:

```
z = ____
p-value = ____
```

It is important to round the test statistic to two decimal places and the p-value to four decimal places as instructed.

**Summary**

This procedure sets up the hypothesis test for determining whether the statement that a minority of Americans decide not to go to college due to financial reasons is supported by the sample data. All relevant conditions are met, ensuring the validity of the test. To reach a conclusion, the test statistic and p-value must be calculated and compared against the significance level.

This

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