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A researcher takes two groups of people. The first group has 140 people, which they call the kontrollgruppe, and the second group has 150 people, which they call the versuchsgruppe. They then run the following experimental procedure: Everyone in the kontrollgruppe is given a difficult problem on workplace efficiency. After thirty minutes, only 20 out of the 140 people managed to come up with a solution that increased workplace efficiency. Everyone in the versuchsgruppe is also given that problem on workplace efficiency. However, they are explicitly told to write a paragraph explaining the problem itself without proposing any solutions for 10 minutes. Then they have 20 minutes to solve the problem. In the versuchsgruppe, 50 people came up with a solution that increased workplace efficiency. Is there a difference between the two methods? Take a 5% significance level. 1. We are comparing two groups, and so it's either going to be a proportion or mean. Are we comparing proportions across two samples or means across two samples? 2. What is the sample size of each sample? Let's call these n1 and n2. 3. How many people in each sample solved the problem? Let's call this x1 and x2. 4. What is the proportion of “solvers" in each group? Call this Pi and p2. 5. What is the combined proportion p= 1t2? ni+n2 6. Find the value of the test statistic for two proportions. 7. Find the critical value associated with a 5% significance level. This is a two-tailed test. 8. Compare the test statistic to the critical value. Should we reject the null hypothesis of there being no difference?

A researcher takes two groups of people. The first group has 140 people, which they call the kontrollgruppe, and the second group has 150 people, which they call the versuchsgruppe. They then run the following experimental procedure: Everyone in the kontrollgruppe is given a difficult problem on workplace efficiency. After thirty minutes, only 20 out of the 140 people managed to come up with a solution that increased workplace efficiency. Everyone in the versuchsgruppe is also given that problem on workplace efficiency. However, they are explicitly told to write a paragraph explaining the problem itself without proposing any solutions for 10 minutes. Then they have 20 minutes to solve the problem. In the versuchsgruppe, 50 people came up with a solution that increased workplace efficiency. Is there a difference between the two methods? Take a 5% significance level. 1. We are comparing two groups, and so it's either going to be a proportion or mean. Are we comparing proportions across two samples or means across two samples? 2. What is the sample size of each sample? Let's call these n1 and n2. 3. How many people in each sample solved the problem? Let's call this x1 and x2. 4. What is the proportion of “solvers" in each group? Call this Pi and p2. 5. What is the combined proportion p= 1t2? ni+n2 6. Find the value of the test statistic for two proportions. 7. Find the critical value associated with a 5% significance level. This is a two-tailed test. 8. Compare the test statistic to the critical value. Should we reject the null hypothesis of there being no difference?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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A researcher takes two groups of people. The first group has 140 people, which they call the kontrollgruppe, and the second group has 150 people, which they call the versuchsgruppe. They then run the following experimental procedure: Everyone in the kontrollgruppe is given a difficult problem on workplace efficiency. After thirty minutes, only 20 out of the 140 people managed to come up with a solution that increased workplace efficiency. Everyone in the versuchsgruppe is also given that problem on workplace efficiency. However, they are explicitly told to write a paragraph explaining the problem itself without proposing any solutions for 10 minutes. Then they have 20 minutes to solve the problem. In the versuchsgruppe, 50 people came up with a solution that increased workplace efficiency. Is there a difference between the two methods? Take a 5% significance level. 1. We are comparing two groups, and so it's either going to be a proportion or mean. Are we comparing proportions across two samples or means across two samples? 2. What is the sample size of each sample? Let's call these nį and n2. 3. How many people in each sample solved the problem? Let's call this x1 and x2. 4. What is the proportion of "solvers" in each group? Call this pi and p2. 5. What is the combined proportion p = ite2? ni+n2 6. Find the value of the test statistic for two proportions. 7. Find the critical value associated with a 5% significance level. This is a two-tailed test. 8. Compare the test statistic to the critical value. Should we reject the null hypothesis of there being no difference?
Transcribed Image Text:A researcher takes two groups of people. The first group has 140 people, which they call the kontrollgruppe, and the second group has 150 people, which they call the versuchsgruppe. They then run the following experimental procedure: Everyone in the kontrollgruppe is given a difficult problem on workplace efficiency. After thirty minutes, only 20 out of the 140 people managed to come up with a solution that increased workplace efficiency. Everyone in the versuchsgruppe is also given that problem on workplace efficiency. However, they are explicitly told to write a paragraph explaining the problem itself without proposing any solutions for 10 minutes. Then they have 20 minutes to solve the problem. In the versuchsgruppe, 50 people came up with a solution that increased workplace efficiency. Is there a difference between the two methods? Take a 5% significance level. 1. We are comparing two groups, and so it's either going to be a proportion or mean. Are we comparing proportions across two samples or means across two samples? 2. What is the sample size of each sample? Let's call these nį and n2. 3. How many people in each sample solved the problem? Let's call this x1 and x2. 4. What is the proportion of "solvers" in each group? Call this pi and p2. 5. What is the combined proportion p = ite2? ni+n2 6. Find the value of the test statistic for two proportions. 7. Find the critical value associated with a 5% significance level. This is a two-tailed test. 8. Compare the test statistic to the critical value. Should we reject the null hypothesis of there being no difference?
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