Homework help ### Skittles Color Frequency AnalysisLina suspects that her children are eating her Skittles candy. Skittles come in red, orange, yellow, green, and purple. Her children prefer specific colors, while Lina has no color preference. To determine if her children have been eating her Skittles, she counts the colors in the bowl that she keeps for herself and records the following results:| Color | Frequency ||---------|-----------|| Red | 25 || Orange | 51 || Yellow | 40 || Green | 50 || Purple | 30 |**Key Information:**- $ k = 5 $ (number of possible outcomes)- $ df = 4 $ (degrees of freedom)Skittles colors are produced in equal proportions (20% for each color) before being mixed and bagged. The question is whether the variation in color frequencies is large enough to argue that someone has been eating Lina's Skittles. ### Objective:Test the claim that the underlying color proportions are different from the advertised proportions of 20% each, implying that the color variations in the bowl are not due to random chance. Use a 1% level of significance.#### Step 1: Determine the Hypotheses1. **The outcome for each of the trials (Skittles) above is the color.** - How many possible outcomes ($ k $) are there per trial? - $ k = 5 $2. **What are the hypothetical proportions for each color?** - $ p = \frac{1}{5} $ for each color3. **Construct the null hypothesis using the answer in Question 2.** - This provides the hypothetical proportions of Skittles for each color.4. **What is the alternative hypothesis?** - The alternative hypothesis is not explicitly given in the steps but would generally be: The proportion of Skittles colors does not match the advertised 20% for each color.This set-up helps determine whether Lina's observation of the Skittles colors deviates significantly from what would be expected if no one had been eating specific colors preferentially. ## Step 2: Collect the Data### 5. Observed FrequenciesThe observed frequencies (**O**) are in the table above. Compute the sample size (**n**) by adding the observed frequencies.\[n = \sum O = \_\_\_\_\_\_\_ \]### 6. Expected FrequenciesThe expected frequencies are each equal to the sample size times the respective proportions in the null hypothesis (**E = np**). Fill in the table below with the appropriate expected frequencies.| Color | **O = Observed** | **E = Expected** ||--------|-------------------|------------------|| Red | 25 | \_\_\_\_\_\_ || Orange | 51 | \_\_\_\_\_\_ || Yellow | 40 | \_\_\_\_\_\_ || Green | 50 | \_\_\_\_\_\_ || Purple | 30 | \_\_\_\_\_\_ |### 7. Conditions for Chi-Square DistributionDo the expected frequencies satisfy the conditions of an approximate $\chi^2$ distribution? Explain.---### 8. Degrees of FreedomWhat are the degrees of freedom for this test?\[df = \_\_\_\_\_\_ \]## Step 3: Assess the Evidence### 9. Compute the Chi-Square Test StatisticCompute the $\chi^2$ test statistic,\[\chi^2 = \sum \frac{(O - E)^2}{E},\]by completing the table below.| Color | **O = Observed** | **E = Expected** | $\frac{(O - E)^2}{E}$ ||--------|-------------------|------------------|-------------------------|| Red | 25 | \_\_\_\_\_\_ | \_\_\_\_\_\_ || Orange | 51 | \_\_\_\_\_\_ | \_\_\_\_\_\_ || Yellow | 40 | \_\_\_\_\_\_ | \_\_\_\_\_\_ || Green | 50 | \_\_\_\_\_\_ | \_\_\_\_\_\_ || Purple | 30 | \_\_\_\_\_\_ | \_\

Name: Homework help ### Skittles Color Frequency AnalysisLina suspects that
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Homework help ### Skittles Color Frequency AnalysisLina suspects that her children are eating her Skittles candy. Skittles come in red, orange, yellow, green, and purple. Her children prefer specific colors, while Lina has no color preference. To det

It is given that the frequencies of the candies. The claim is that the underlying color proportions…

Math

Statistics

Lina has reason to believe that her children are eating her Skittles candy. Skittles come in red, orange, yellow, green, and purple. Her children all have color preferences, but Lina has no color preference. In order to prove the guilt of her children, she counts the colors in the bowl that she keeps out, with the following results.

Lina has reason to believe that her children are eating her Skittles candy. Skittles come in red, orange, yellow, green, and purple. Her children all have color preferences, but Lina has no color preference. In order to prove the guilt of her children, she counts the colors in the bowl that she keeps out, with the following results.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: rest

Q: Question 3

Q: parts iv and v please

A: Given is a question on the probability of failure/success. Number of failed O-rings 0 1 2 3 4 5 6…

Q: Vx - 3 dx x=3

Q: im 2. 3. 2.

Q: Part A thought G

A: Note: Since we only answer up to 3 subparts , we will answer the first 3. Please resubmit the…

Q: Help!! Answer correctly

Q: fy-? 4- メーh)

Q: accomplishment

Q: If two lines in the coordinate plane are perpendicular, then their slopes are In other words, For…

A: If two lines in a coordinate plane are perpendicular then their slopes are negative reciprocal of…

Q: domain

A: Consider a function

Q: style

Q: A large speaker that you are planning to use, has a huge diaphragm connected to a spring, the force…

Q: profit nal Mar

A: Given, A product has cost function Cx=x2-2x and revenue function Rx=10x , where x…

Q: Calculus

A: The solution is given below in the next steps:

Q: Part 1,2,3

A: The point is, 6,-2 So, the point is in 4th quadrant.

Q: Help break down

A: We have to find mean and stanadard deviation..

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Topic Video

Question

Homework help

### Skittles Color Frequency Analysis

Lina suspects that her children are eating her Skittles candy. Skittles come in red, orange, yellow, green, and purple. Her children prefer specific colors, while Lina has no color preference. To determine if her children have been eating her Skittles, she counts the colors in the bowl that she keeps for herself and records the following results:

| Color | Frequency |
|---------|-----------|
| Red | 25 |
| Orange | 51 |
| Yellow | 40 |
| Green | 50 |
| Purple | 30 |

**Key Information:**
- $ k = 5 $ (number of possible outcomes)
- $ df = 4 $ (degrees of freedom)

Skittles colors are produced in equal proportions (20% for each color) before being mixed and bagged. The question is whether the variation in color frequencies is large enough to argue that someone has been eating Lina's Skittles.

### Objective:
Test the claim that the underlying color proportions are different from the advertised proportions of 20% each, implying that the color variations in the bowl are not due to random chance. Use a 1% level of significance.

#### Step 1: Determine the Hypotheses

1. **The outcome for each of the trials (Skittles) above is the color.**
- How many possible outcomes ($ k $) are there per trial?
- $ k = 5 $

2. **What are the hypothetical proportions for each color?**
- $ p = \frac{1}{5} $ for each color

3. **Construct the null hypothesis using the answer in Question 2.**
- This provides the hypothetical proportions of Skittles for each color.

4. **What is the alternative hypothesis?**
- The alternative hypothesis is not explicitly given in the steps but would generally be: The proportion of Skittles colors does not match the advertised 20% for each color.

This set-up helps determine whether Lina's observation of the Skittles colors deviates significantly from what would be expected if no one had been eating specific colors preferentially.

## Step 2: Collect the Data

### 5. Observed Frequencies
The observed frequencies (**O**) are in the table above. Compute the sample size (**n**) by adding the observed frequencies.

\[n = \sum O = \_\_\_\_\_\_\_ \]

### 6. Expected Frequencies
The expected frequencies are each equal to the sample size times the respective proportions in the null hypothesis (**E = np**). Fill in the table below with the appropriate expected frequencies.

| Color | **O = Observed** | **E = Expected** |
|--------|-------------------|------------------|
| Red | 25 | \_\_\_\_\_\_ |
| Orange | 51 | \_\_\_\_\_\_ |
| Yellow | 40 | \_\_\_\_\_\_ |
| Green | 50 | \_\_\_\_\_\_ |
| Purple | 30 | \_\_\_\_\_\_ |

### 7. Conditions for Chi-Square Distribution
Do the expected frequencies satisfy the conditions of an approximate $\chi^2$ distribution? Explain.

---

### 8. Degrees of Freedom
What are the degrees of freedom for this test?

\[df = \_\_\_\_\_\_ \]

## Step 3: Assess the Evidence

### 9. Compute the Chi-Square Test Statistic
Compute the $\chi^2$ test statistic,

\[
\chi^2 = \sum \frac{(O - E)^2}{E},
\]

by completing the table below.

| Color | **O = Observed** | **E = Expected** | $\frac{(O - E)^2}{E}$ |
|--------|-------------------|------------------|-------------------------|
| Red | 25 | \_\_\_\_\_\_ | \_\_\_\_\_\_ |
| Orange | 51 | \_\_\_\_\_\_ | \_\_\_\_\_\_ |
| Yellow | 40 | \_\_\_\_\_\_ | \_\_\_\_\_\_ |
| Green | 50 | \_\_\_\_\_\_ | \_\_\_\_\_\_ |
| Purple | 30 | \_\_\_\_\_\_ | \_\

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Algebraic Operations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Briefly explain the purpose of research. ?
Need help with part 3
part c pls
help ?
It 3. Mow
Thank you.
Help with
HELP HELP HELP
help with these
Sub part 6
Math help
Help please! The Medieval Europe How important is preservation of historical texts? How did the materials during this time period survive? What are current methods of preservation?