Suppose that, on average, U.S. adults get fast food 10 times a week. In a random sample of 41 people, it was found that they ordered fast food an average of 9 times in one week. Assume the population standard deviation is 4.4. Perform a test at a significance level of 5% to determine whether or not the number of times a U.S. adult gets fast food in a week is different from 10. a. Check all of the requirements that are satisfied. random the distribution is normal since n ≥ 30 the distribution is normal since the a distribution is normal the p distribution is normal since np > 10 and nq ≥ 10 b. Identify the null and alternative hypotheses.
Suppose that, on average, U.S. adults get fast food 10 times a week. In a random sample of 41 people, it was found that they ordered fast food an average of 9 times in one week. Assume the population standard deviation is 4.4. Perform a test at a significance level of 5% to determine whether or not the number of times a U.S. adult gets fast food in a week is different from 10. a. Check all of the requirements that are satisfied. random the distribution is normal since n ≥ 30 the distribution is normal since the a distribution is normal the p distribution is normal since np > 10 and nq ≥ 10 b. Identify the null and alternative hypotheses.
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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![### Statistical Analysis of Fast Food Consumption
**Scenario:**
Suppose that, on average, U.S. adults get fast food 10 times a week. In a random sample of 41 people, it was found that they ordered fast food an average of 9 times in one week. Assume the population standard deviation is 4.4. Perform a test at a significance level of 5% to determine whether or not the number of times a U.S. adult gets fast food in a week is different from 10.
**Requirements Check:**
a. Check all of the requirements that are satisfied.
- [x] **Random**: The sample was randomly selected.
- [x] **The \(\bar{x}\) distribution is normal since \(n \geq 30\)**: The sample size is 41 which is greater than 30, implying the sample mean distribution is approximately normal.
- [ ] **The \(\bar{x}\) distribution is normal since the \(x\) distribution is normal**: This requirement is not checked.
- [ ] **The \(\hat{p}\) distribution is normal since \(np \geq 10\) and \(nq \geq 10\)**: This is related to proportions and is not applicable here.
**Hypotheses:**
b. Identify the null and alternative hypotheses.
- **Null Hypothesis (\(H_0\))**: The average number of times a U.S. adult gets fast food in a week is 10.
- **Alternative Hypothesis (\(H_a\))**: The average number of times a U.S. adult gets fast food in a week is not 10.
This test will help in identifying any significant difference from the assumed average, using a standard significance level of 5%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe76b69af-9a2c-4c6c-92e8-18acb680d06b%2F2edc6ed4-2ba1-47ba-aadf-f23439697e6d%2F4aspleg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Fast Food Consumption
**Scenario:**
Suppose that, on average, U.S. adults get fast food 10 times a week. In a random sample of 41 people, it was found that they ordered fast food an average of 9 times in one week. Assume the population standard deviation is 4.4. Perform a test at a significance level of 5% to determine whether or not the number of times a U.S. adult gets fast food in a week is different from 10.
**Requirements Check:**
a. Check all of the requirements that are satisfied.
- [x] **Random**: The sample was randomly selected.
- [x] **The \(\bar{x}\) distribution is normal since \(n \geq 30\)**: The sample size is 41 which is greater than 30, implying the sample mean distribution is approximately normal.
- [ ] **The \(\bar{x}\) distribution is normal since the \(x\) distribution is normal**: This requirement is not checked.
- [ ] **The \(\hat{p}\) distribution is normal since \(np \geq 10\) and \(nq \geq 10\)**: This is related to proportions and is not applicable here.
**Hypotheses:**
b. Identify the null and alternative hypotheses.
- **Null Hypothesis (\(H_0\))**: The average number of times a U.S. adult gets fast food in a week is 10.
- **Alternative Hypothesis (\(H_a\))**: The average number of times a U.S. adult gets fast food in a week is not 10.
This test will help in identifying any significant difference from the assumed average, using a standard significance level of 5%.
![## Hypothesis Testing Worksheet
**a. Null Hypothesis (\( H_0 \)):**
Select an answer: \( = \), \( < \), \( > \)
**b. Alternative Hypothesis (\( H_1 \)):**
Select an answer: \( \neq \), \( < \), \( > \)
**c. What type of hypothesis test should you conduct (left, right, or two-tailed)?**
- \( \circ \) Left-tailed
- \( \circ \) Right-tailed
- \( \circ \) Two-tailed
**d. Identify the appropriate significance level. Make sure to enter your answer as a decimal.**
\( \underline{\phantom{XX}} \)
**e. [Irrelevant section removed]**
**f. Find the test statistic. Write the result below, and be sure to round your final answer to two decimal places.**
\( \underline{\phantom{XX}} \)
**g. Find the critical value. Round your answer to 2 decimal places.**
\( \underline{\phantom{XX}} \)
**h. Should you reject or not reject the null hypothesis?**
- \( \circ \) Reject the null hypothesis since \( p\text{-value} \leq \alpha \)
- \( \circ \) Do not reject the null hypothesis since \( p\text{-value} > \alpha \)
- \( \circ \) Reject the null hypothesis since the test statistic is inside the critical region
- \( \circ \) Do not reject the null hypothesis since the test statistic is outside the critical region
**i. Select the statement below that best represents the interpretation.**
- \( \circ \) There is sufficient evidence to support the claim that the amount of times U.S. adults order fast food is different than 10.
- \( \circ \) There is not sufficient evidence to support the claim that the amount of times U.S. adults order fast food is different than 10.
- \( \circ \) The sample data support the claim that U.S. adults get fast food 10 times a week.
- \( \circ \) We accept the claim that U.S. adults get fast food 10 times a week.
This worksheet guides you through the steps of hypothesis testing, helping determine the validity of a claim based on sample data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe76b69af-9a2c-4c6c-92e8-18acb680d06b%2F2edc6ed4-2ba1-47ba-aadf-f23439697e6d%2Fj1ag07l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing Worksheet
**a. Null Hypothesis (\( H_0 \)):**
Select an answer: \( = \), \( < \), \( > \)
**b. Alternative Hypothesis (\( H_1 \)):**
Select an answer: \( \neq \), \( < \), \( > \)
**c. What type of hypothesis test should you conduct (left, right, or two-tailed)?**
- \( \circ \) Left-tailed
- \( \circ \) Right-tailed
- \( \circ \) Two-tailed
**d. Identify the appropriate significance level. Make sure to enter your answer as a decimal.**
\( \underline{\phantom{XX}} \)
**e. [Irrelevant section removed]**
**f. Find the test statistic. Write the result below, and be sure to round your final answer to two decimal places.**
\( \underline{\phantom{XX}} \)
**g. Find the critical value. Round your answer to 2 decimal places.**
\( \underline{\phantom{XX}} \)
**h. Should you reject or not reject the null hypothesis?**
- \( \circ \) Reject the null hypothesis since \( p\text{-value} \leq \alpha \)
- \( \circ \) Do not reject the null hypothesis since \( p\text{-value} > \alpha \)
- \( \circ \) Reject the null hypothesis since the test statistic is inside the critical region
- \( \circ \) Do not reject the null hypothesis since the test statistic is outside the critical region
**i. Select the statement below that best represents the interpretation.**
- \( \circ \) There is sufficient evidence to support the claim that the amount of times U.S. adults order fast food is different than 10.
- \( \circ \) There is not sufficient evidence to support the claim that the amount of times U.S. adults order fast food is different than 10.
- \( \circ \) The sample data support the claim that U.S. adults get fast food 10 times a week.
- \( \circ \) We accept the claim that U.S. adults get fast food 10 times a week.
This worksheet guides you through the steps of hypothesis testing, helping determine the validity of a claim based on sample data.
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