Specify the null and alternative hypotheses. Let the first group be the consumers assigned to the flex position, and let the second group be the consumers assigned to the extended position.
Specify the null and alternative hypotheses. Let the first group be the consumers assigned to the flex position, and let the second group be the consumers assigned to the extended position.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 3BGP
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Topic Video
Question
12) p value
![### Hypothesis Testing for Vice Product Purchasing Behavior
**Objective:**
Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a shopping basket) compared to when your arm is extended (as when pushing a shopping cart).
**Method:**
To test this theory, the researchers conducted an experiment with 26 consumers.
- **Group Assignment:** The participants were divided into two groups:
- **Flex Position Group:** This group pushed their hand against a table in a flex position (similar to carrying a shopping basket).
- **Extended Position Group:** This group pushed their hand against a table in an extended position (similar to pushing a shopping cart).
- **Task:** Participants were asked a series of shopping questions and were offered several choices between a vice and a virtue (e.g., a movie ticket vs. a shopping coupon, paying now vs. paying later). For each participant, a choice score (on a scale from 0 to 100) was determined, with higher scores indicating a greater preference for vice options.
**Results:**
- **Flexed Arm Group:** The average choice score was 62.
- **Extended Arm Group:** The average choice score was 43.
- **Standard Deviations:**
- Flexed arm: 7
- Extended arm: 14
**Research Question:**
Does this information support the researchers’ theory that arm position affects the likelihood of purchasing vice products?
**Hypothesis Testing:**
**Null Hypothesis (H₀):**
\[
\mu_1 - \mu_2 = 0
\]
(The difference in average choice scores between the flex and extended positions is zero, indicating no effect of arm position.)
**Alternative Hypothesis (H₁):**
\[
\mu_1 - \mu_2 > 0
\]
(The average choice score for the flex position is greater than the extended position, indicating a tendency to choose vice products with a flexed arm.)
**Computations:**
1. **Test Statistic:**
\[
\text{The test statistic is} \quad 4.38
\]
(Value rounded to two decimal places as needed.)
2. **P-value Calculation:**
\[
p = \quad (\text{Round to three decimal places as needed.})
\]
This p](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0dffadf4-6195-4ecd-8325-0f00263ddf75%2F5ce42459-81f9-4844-86f2-22f7a41190fc%2Fmvgsfvc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Vice Product Purchasing Behavior
**Objective:**
Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a shopping basket) compared to when your arm is extended (as when pushing a shopping cart).
**Method:**
To test this theory, the researchers conducted an experiment with 26 consumers.
- **Group Assignment:** The participants were divided into two groups:
- **Flex Position Group:** This group pushed their hand against a table in a flex position (similar to carrying a shopping basket).
- **Extended Position Group:** This group pushed their hand against a table in an extended position (similar to pushing a shopping cart).
- **Task:** Participants were asked a series of shopping questions and were offered several choices between a vice and a virtue (e.g., a movie ticket vs. a shopping coupon, paying now vs. paying later). For each participant, a choice score (on a scale from 0 to 100) was determined, with higher scores indicating a greater preference for vice options.
**Results:**
- **Flexed Arm Group:** The average choice score was 62.
- **Extended Arm Group:** The average choice score was 43.
- **Standard Deviations:**
- Flexed arm: 7
- Extended arm: 14
**Research Question:**
Does this information support the researchers’ theory that arm position affects the likelihood of purchasing vice products?
**Hypothesis Testing:**
**Null Hypothesis (H₀):**
\[
\mu_1 - \mu_2 = 0
\]
(The difference in average choice scores between the flex and extended positions is zero, indicating no effect of arm position.)
**Alternative Hypothesis (H₁):**
\[
\mu_1 - \mu_2 > 0
\]
(The average choice score for the flex position is greater than the extended position, indicating a tendency to choose vice products with a flexed arm.)
**Computations:**
1. **Test Statistic:**
\[
\text{The test statistic is} \quad 4.38
\]
(Value rounded to two decimal places as needed.)
2. **P-value Calculation:**
\[
p = \quad (\text{Round to three decimal places as needed.})
\]
This p
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