The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep Age Fewer than 6 6 to 6.9 7 to 7.9 8 or more Total 49 or younger 37 59 76 68 240 50 or older 33 60 76 91 260 a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use a = .05. Use Table 12.4. Compute the value of the X 2 test statistic (to 2 decimals). The p value is greater than .10 What is your conclusion? Cannot reject the assumption that age and hours of sleep are independent V b. Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal). Less than 6 hours % 6 to 6.9 hours % 7 to 7.9 hours % 8 or more hours %
The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep Age Fewer than 6 6 to 6.9 7 to 7.9 8 or more Total 49 or younger 37 59 76 68 240 50 or older 33 60 76 91 260 a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use a = .05. Use Table 12.4. Compute the value of the X 2 test statistic (to 2 decimals). The p value is greater than .10 What is your conclusion? Cannot reject the assumption that age and hours of sleep are independent V b. Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal). Less than 6 hours % 6 to 6.9 hours % 7 to 7.9 hours % 8 or more hours %
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![**Title: Analysis of Sleep Patterns Based on Age**
The National Sleep Foundation conducted a survey to assess whether the number of hours individuals sleep per night is independent of age (Newsweek, January 19, 2004). The data below shows the distribution of sleep hours for individuals aged 49 and younger, and for those aged 50 and older.
**Table: Hours of Sleep**
| Age Group | Fewer than 6 | 6 to 6.9 | 7 to 7.9 | 8 or more | Total |
|----------------|--------------|----------|----------|-----------|-------|
| 49 or younger | 37 | 59 | 76 | 68 | 240 |
| 50 or older | 33 | 60 | 76 | 91 | 260 |
**a. Test of Independence**
A test of independence was conducted to determine if sleep hours on weeknights are independent of age. Using a significance level of α = 0.05, and referencing Table 12.4:
- Compute the value of the Chi-Square (χ²) test statistic (rounded to 2 decimals).
- The p-value is determined to be greater than 0.10.
- **Conclusion:** We cannot reject the assumption that age and hours of sleep are independent.
**b. Percentage Estimation**
For a total sample size of 500, estimate the percentage of people who sleep:
- Less than 6 hours: [Input Percent] %
- 6 to 6.9 hours: [Input Percent] %
- 7 to 7.9 hours: [Input Percent] %
- 8 or more hours: [Input Percent] %
These calculations provide insights into the sleep patterns across different age groups and help to understand any differences based on age.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd36b6842-f013-4a5d-8d88-3ce050696fab%2Fe42daa6a-0c01-43c7-a716-226e4f1cbc58%2F378icja_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Analysis of Sleep Patterns Based on Age**
The National Sleep Foundation conducted a survey to assess whether the number of hours individuals sleep per night is independent of age (Newsweek, January 19, 2004). The data below shows the distribution of sleep hours for individuals aged 49 and younger, and for those aged 50 and older.
**Table: Hours of Sleep**
| Age Group | Fewer than 6 | 6 to 6.9 | 7 to 7.9 | 8 or more | Total |
|----------------|--------------|----------|----------|-----------|-------|
| 49 or younger | 37 | 59 | 76 | 68 | 240 |
| 50 or older | 33 | 60 | 76 | 91 | 260 |
**a. Test of Independence**
A test of independence was conducted to determine if sleep hours on weeknights are independent of age. Using a significance level of α = 0.05, and referencing Table 12.4:
- Compute the value of the Chi-Square (χ²) test statistic (rounded to 2 decimals).
- The p-value is determined to be greater than 0.10.
- **Conclusion:** We cannot reject the assumption that age and hours of sleep are independent.
**b. Percentage Estimation**
For a total sample size of 500, estimate the percentage of people who sleep:
- Less than 6 hours: [Input Percent] %
- 6 to 6.9 hours: [Input Percent] %
- 7 to 7.9 hours: [Input Percent] %
- 8 or more hours: [Input Percent] %
These calculations provide insights into the sleep patterns across different age groups and help to understand any differences based on age.
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