In a previous poll, 47% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 497 of 1106 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a = 0.01 significance level. Because npo (1-Po) = (1) 10 and the sample size is (2). 5% of the population size, and the sample (3) satisfied. the requirements for testing the hypothesis (4). (Round to one decimal place as needed.) What are the null and alternative hypotheses? Họ: (5). (6). versus H,: (7). (8) (Type integers or decimals. Do not round.) Find the test statistic, zo. Zo = (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Choose the correct answer below. O A. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the O B. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the nu OC. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, do not rejec O D. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, do not re (2) O greater than O can be reasonably assumed to be random, O is given to be random, (1) O < (3) (4) O are O less than O are not is given to not be random, cannot be reasonably assumed to be random, (5) O o (6) O # (7) O p (8) O p 0000 0000 0000
In a previous poll, 47% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 497 of 1106 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a = 0.01 significance level. Because npo (1-Po) = (1) 10 and the sample size is (2). 5% of the population size, and the sample (3) satisfied. the requirements for testing the hypothesis (4). (Round to one decimal place as needed.) What are the null and alternative hypotheses? Họ: (5). (6). versus H,: (7). (8) (Type integers or decimals. Do not round.) Find the test statistic, zo. Zo = (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Choose the correct answer below. O A. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the O B. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the nu OC. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, do not rejec O D. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, do not re (2) O greater than O can be reasonably assumed to be random, O is given to be random, (1) O < (3) (4) O are O less than O are not is given to not be random, cannot be reasonably assumed to be random, (5) O o (6) O # (7) O p (8) O p 0000 0000 0000
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: Testing Hypotheses on Family Dinner Frequency**
**Problem Context:**
In a previous poll, 47% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 497 of 1106 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the \( \alpha = 0.01 \) significance level.
**Statistical Analysis Steps:**
1. **Requirements Verification:**
- Compute \( np_0 (1 - p_0) \) and sample size relative to population size:
- \( np_0 (1 - p_0) = \) _________ \( (1) \) [Choice: greater than / less than] 10
- Sample size \( (2) \) [Choice: greater than / less than] 5% of the population size.
- Determine if sample \( (3) \) [Choice: can be reasonably assumed to be random, is given to be random, cannot be reasonably assumed to be random]
- Determine if requirements for testing the hypothesis \( (4) \) [Choice: are / are not] satisfied.
- (Round to one decimal place as needed.)
2. **Hypotheses Formulation:**
- Null Hypothesis \( H_0: \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
- Statement \( (5) \) [Choice: \( p \), \( \mu \), \( \sigma \)] \( (6) \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
- Alternative Hypothesis \( H_1: \)
- Statement \( (7) \) [Choice: \( p \), \( \mu \), \( \sigma \)] \( (8) \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
3. **Determine Test Statistic:**
- Compute \( z_0 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae8e0e00-e909-4cd4-8a43-4c71501433ad%2F6404d81e-c495-45f2-ad22-cf21e146d5e4%2F98rzbng_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is a transcription of the text provided in the image, structured as for an educational website:
---
**Statistical Analysis: Testing Hypotheses on Family Dinner Frequency**
**Problem Context:**
In a previous poll, 47% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 497 of 1106 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the \( \alpha = 0.01 \) significance level.
**Statistical Analysis Steps:**
1. **Requirements Verification:**
- Compute \( np_0 (1 - p_0) \) and sample size relative to population size:
- \( np_0 (1 - p_0) = \) _________ \( (1) \) [Choice: greater than / less than] 10
- Sample size \( (2) \) [Choice: greater than / less than] 5% of the population size.
- Determine if sample \( (3) \) [Choice: can be reasonably assumed to be random, is given to be random, cannot be reasonably assumed to be random]
- Determine if requirements for testing the hypothesis \( (4) \) [Choice: are / are not] satisfied.
- (Round to one decimal place as needed.)
2. **Hypotheses Formulation:**
- Null Hypothesis \( H_0: \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
- Statement \( (5) \) [Choice: \( p \), \( \mu \), \( \sigma \)] \( (6) \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
- Alternative Hypothesis \( H_1: \)
- Statement \( (7) \) [Choice: \( p \), \( \mu \), \( \sigma \)] \( (8) \) [Choice: \( = \), \( \neq \), \( < \), \( > \)]
3. **Determine Test Statistic:**
- Compute \( z_0 \)
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