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thus pick the photo of the correct solution more often than what would be done by random chance. a. Describe the parameter of interest in the context of this study and assign a symbol to denote it. b. What is the observed value of the statistic in this case? c. Write out the null and alternative hypotheses for this first in words and then in symbols. d. We conducted a test of significance using the One Pro- portion applet and got the following null distribution for the "number of heads." (Note: this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) Based on the null distribution, what is the p-value for the test? How did you calculate it? Probability of heads: 0.5 Number of tosses: 8 Number of repetitions: 100 O Animate Toss Coins Total = 100 40 30 20 10 1 2 3 4 5 6 7 8 Number of heads e. Based on your p-value, do you have strong evidence that Sarah understands how to solve problems similar to those she was presented? How are you deciding? Justify. f. Complete this sentence describing what the p-value means: If Sarah doesn't understand how to solve prob- lems and is just guessing at which picture to select, the probability she would ... g. What does a single dot in the null distribution represent in terms of Sarah and the photos?

thus pick the photo of the correct solution more often than what would be done by random chance. a. Describe the parameter of interest in the context of this study and assign a symbol to denote it. b. What is the observed value of the statistic in this case? c. Write out the null and alternative hypotheses for this first in words and then in symbols. d. We conducted a test of significance using the One Pro- portion applet and got the following null distribution for the "number of heads." (Note: this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) Based on the null distribution, what is the p-value for the test? How did you calculate it? Probability of heads: 0.5 Number of tosses: 8 Number of repetitions: 100 O Animate Toss Coins Total = 100 40 30 20 10 1 2 3 4 5 6 7 8 Number of heads e. Based on your p-value, do you have strong evidence that Sarah understands how to solve problems similar to those she was presented? How are you deciding? Justify. f. Complete this sentence describing what the p-value means: If Sarah doesn't understand how to solve prob- lems and is just guessing at which picture to select, the probability she would ... g. What does a single dot in the null distribution represent in terms of Sarah and the photos?

MATLAB: An Introduction with Applications
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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**Sarah the Chimpanzee** **1.2.12** A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented. We want to run a test of significance to determine whether Sarah understands how to solve problems and will select the appropriate solution.
Transcribed Image Text:**Sarah the Chimpanzee** **1.2.12** A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented. We want to run a test of significance to determine whether Sarah understands how to solve problems and will select the appropriate solution.
### Educational Exercise on Probability and Hypothesis Testing #### Context of Study The study aims to assess whether Sarah can pick the photo of the correct solution more often than random chance would suggest. #### Questions and Analysis **a. Parameter of Interest** - **Description**: The parameter of interest is the proportion of correct photos Sarah picks. - **Symbol**: Denote this parameter as \( p \). **b. Observed Value of the Statistic** - **Value**: Determine the actual proportion of correct photos selected by Sarah. **c. Null and Alternative Hypotheses** - **In Words**: - **Null Hypothesis (\( H_0 \))**: Sarah's choices are random, i.e., \( p = 0.5 \). - **Alternative Hypothesis (\( H_a \))**: Sarah picks the correct photo more frequently, i.e., \( p > 0.5 \). - **In Symbols**: - \( H_0: p = 0.5 \) - \( H_a: p > 0.5 \) **d. Test of Significance Using One Proportion Applet** - **Setup**: - **Probability of heads**: 0.5 - **Number of tosses**: 8 - **Number of repetitions**: 100 - **Graph Explanation**: - The graph represents the null distribution for the "number of heads" in 100 simulated samples, each with 8 tosses. - The distribution resembles a binomial distribution with a peak at 4, indicating the most common outcome is 4 heads. - **p-value Calculation**: The p-value is determined by evaluating where Sarah's observed statistic lies in the null distribution. **e. Evaluating the Evidence** - **Question**: Based on your p-value, do you have strong evidence that Sarah understands how to solve similar problems better than by guessing? - **Decision Making**: Compare the p-value to a significance level (e.g., 0.05) to determine if the null hypothesis can be rejected. **f. p-value Interpretation** - **Sentence Completion**: If Sarah doesn't understand how to solve problems and is guessing, the probability she would... exceed or match the observed number of correct picks is the p-value. **g. Representation of a Single Dot** - **Meaning**: Each dot in the null
Transcribed Image Text:### Educational Exercise on Probability and Hypothesis Testing #### Context of Study The study aims to assess whether Sarah can pick the photo of the correct solution more often than random chance would suggest. #### Questions and Analysis **a. Parameter of Interest** - **Description**: The parameter of interest is the proportion of correct photos Sarah picks. - **Symbol**: Denote this parameter as \( p \). **b. Observed Value of the Statistic** - **Value**: Determine the actual proportion of correct photos selected by Sarah. **c. Null and Alternative Hypotheses** - **In Words**: - **Null Hypothesis (\( H_0 \))**: Sarah's choices are random, i.e., \( p = 0.5 \). - **Alternative Hypothesis (\( H_a \))**: Sarah picks the correct photo more frequently, i.e., \( p > 0.5 \). - **In Symbols**: - \( H_0: p = 0.5 \) - \( H_a: p > 0.5 \) **d. Test of Significance Using One Proportion Applet** - **Setup**: - **Probability of heads**: 0.5 - **Number of tosses**: 8 - **Number of repetitions**: 100 - **Graph Explanation**: - The graph represents the null distribution for the "number of heads" in 100 simulated samples, each with 8 tosses. - The distribution resembles a binomial distribution with a peak at 4, indicating the most common outcome is 4 heads. - **p-value Calculation**: The p-value is determined by evaluating where Sarah's observed statistic lies in the null distribution. **e. Evaluating the Evidence** - **Question**: Based on your p-value, do you have strong evidence that Sarah understands how to solve similar problems better than by guessing? - **Decision Making**: Compare the p-value to a significance level (e.g., 0.05) to determine if the null hypothesis can be rejected. **f. p-value Interpretation** - **Sentence Completion**: If Sarah doesn't understand how to solve problems and is guessing, the probability she would... exceed or match the observed number of correct picks is the p-value. **g. Representation of a Single Dot** - **Meaning**: Each dot in the null
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