A magazine presented a lesson in hypothesis testing carried out by medical students in a biostatistics class. Students were blind-folded and then given a red-colored or yellow-colored gummy bear to chew. (Half the students were randomly assigned to receive the red gummy bear and half to receive the yellow bear. The students could not see what color gummy bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 159 students who participated in the study, 100 correctly identified the color of the gummy bear. Complete parts a through c below. a. If there is no relationship between color and gummy bear flavor, what proportion of the population of students will correctly identify the color? 0.5 (Type an integer or a decimal. Do not round.) b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Let p be the true proportion of students who are able to correctly identify the color of the gummy bear. Họ: p = 0.5 H:p + 0.5 (Type integers or decimals. Do not round.) c. Carry out the test and give the appropriate conclusion at a = 0.01. Use the p-value of the test to make your decision. Identify the test statistic for this test. (Round to two decimal places as needed.)
A magazine presented a lesson in hypothesis testing carried out by medical students in a biostatistics class. Students were blind-folded and then given a red-colored or yellow-colored gummy bear to chew. (Half the students were randomly assigned to receive the red gummy bear and half to receive the yellow bear. The students could not see what color gummy bear they were given.) After chewing, the students were asked to guess the color of the candy based on the flavor. Of the 159 students who participated in the study, 100 correctly identified the color of the gummy bear. Complete parts a through c below. a. If there is no relationship between color and gummy bear flavor, what proportion of the population of students will correctly identify the color? 0.5 (Type an integer or a decimal. Do not round.) b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Let p be the true proportion of students who are able to correctly identify the color of the gummy bear. Họ: p = 0.5 H:p + 0.5 (Type integers or decimals. Do not round.) c. Carry out the test and give the appropriate conclusion at a = 0.01. Use the p-value of the test to make your decision. Identify the test statistic for this test. (Round to two decimal places as needed.)
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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![### Hypothesis Testing Lesson: Color and Flavor Relationship in Gummy Bears
#### Study Overview
A magazine presented a lesson in hypothesis testing conducted by medical students in a biostatistics class. The students were blindfolded and given either a red-colored or yellow-colored gummy bear to chew. Each student was randomly assigned to either the red or yellow gummy bear group. After chewing, the students were asked to guess the color of the gummy bear based solely on its flavor. Out of the 159 students who participated, 100 correctly identified the color of the gummy bear.
#### Hypothesis Testing Exercise
**a. Calculating Proportion for Correct Identification:**
If there is no relationship between the color and the gummy bear flavor, the expected proportion of students who correctly identify the color is:
\[ 0.5 \]
\[ \text{(Type an integer or a decimal. Do not round.)} \]
**b. Null and Alternative Hypotheses:**
Under the hypothesis that the color and the flavor of the gummy bear are not related, we define \( p \) as the true proportion of students who can correctly identify the color of the gummy bear based on its flavor.
- Null Hypothesis (H₀):
\[ H_0: p = 0.5 \]
- Alternative Hypothesis (Hₐ):
\[ H_a: p \neq 0.5 \]
\[ \text{(Type integers or decimals. Do not round.)} \]
**c. Testing at Significance Level α = 0.01:**
To test the hypotheses, we carry out the test using a significance level (\( α \)) of 0.01. The decision will be based on the p-value of the test.
**Identify the test statistic:**
\[ \text{(Round to two decimal places as needed.)} \]
Unfortunately, the exact test statistic value and the subsequent conclusion are not provided in the image, so further information and steps must be followed to complete this hypothesis testing. Those steps would typically involve calculating the test statistic using the sample proportion and comparing it against a critical value or using the p-value to make a rejection decision at the given significance level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d0fca7b-87e2-42be-9458-260269753889%2F335b1255-0c37-4257-8f17-07471af43afe%2F2dkdt5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing Lesson: Color and Flavor Relationship in Gummy Bears
#### Study Overview
A magazine presented a lesson in hypothesis testing conducted by medical students in a biostatistics class. The students were blindfolded and given either a red-colored or yellow-colored gummy bear to chew. Each student was randomly assigned to either the red or yellow gummy bear group. After chewing, the students were asked to guess the color of the gummy bear based solely on its flavor. Out of the 159 students who participated, 100 correctly identified the color of the gummy bear.
#### Hypothesis Testing Exercise
**a. Calculating Proportion for Correct Identification:**
If there is no relationship between the color and the gummy bear flavor, the expected proportion of students who correctly identify the color is:
\[ 0.5 \]
\[ \text{(Type an integer or a decimal. Do not round.)} \]
**b. Null and Alternative Hypotheses:**
Under the hypothesis that the color and the flavor of the gummy bear are not related, we define \( p \) as the true proportion of students who can correctly identify the color of the gummy bear based on its flavor.
- Null Hypothesis (H₀):
\[ H_0: p = 0.5 \]
- Alternative Hypothesis (Hₐ):
\[ H_a: p \neq 0.5 \]
\[ \text{(Type integers or decimals. Do not round.)} \]
**c. Testing at Significance Level α = 0.01:**
To test the hypotheses, we carry out the test using a significance level (\( α \)) of 0.01. The decision will be based on the p-value of the test.
**Identify the test statistic:**
\[ \text{(Round to two decimal places as needed.)} \]
Unfortunately, the exact test statistic value and the subsequent conclusion are not provided in the image, so further information and steps must be followed to complete this hypothesis testing. Those steps would typically involve calculating the test statistic using the sample proportion and comparing it against a critical value or using the p-value to make a rejection decision at the given significance level.
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