The population standard deviation for number of hours of sleep that people get per night is 1.3 hours. You are interested in finding a 95% confidence interval for the mean amount of sleep people who do not drink coffee get. The data below show the results of the survey that you took. Assume that the standard deviation for people who do not drink coffee is the same as the standard deviation for the general population. 6,8,7,8,8,7,9,5,7,8,6,7,8 Assume a normal distribution and round your answers to two decimal places. A. To compute the confidence interval, use the [Select] distribution. B. With 95% confidence the mean number of hours that people who do not drink coffee get is between [Select ] and [Select] C. If many groups of 13 randomly selected people who do not drink coffee are surveyed, then a different confidence interval would be produced from each group. About [Select] percent of these confidence intervals will contain the true population mean number of hours of sleen per night and about [Select]
The population standard deviation for number of hours of sleep that people get per night is 1.3 hours. You are interested in finding a 95% confidence interval for the mean amount of sleep people who do not drink coffee get. The data below show the results of the survey that you took. Assume that the standard deviation for people who do not drink coffee is the same as the standard deviation for the general population. 6,8,7,8,8,7,9,5,7,8,6,7,8 Assume a normal distribution and round your answers to two decimal places. A. To compute the confidence interval, use the [Select] distribution. B. With 95% confidence the mean number of hours that people who do not drink coffee get is between [Select ] and [Select] C. If many groups of 13 randomly selected people who do not drink coffee are surveyed, then a different confidence interval would be produced from each group. About [Select] percent of these confidence intervals will contain the true population mean number of hours of sleen per night and about [Select]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![### Calculating Confidence Interval for Sleep Hours of Non-Coffee Drinkers
The population standard deviation for the number of hours of sleep that people get per night is 1.3 hours. You are interested in finding a 95% confidence interval for the mean amount of sleep people who do not drink coffee get. The following data shows the results of a survey:
**Data Set:**
6, 8, 7, 8, 8, 7, 9, 5, 7, 8, 6, 7, 8
**Assumptions:**
- The standard deviation for people who do not drink coffee is the same as the standard deviation for the general population.
- Assume a normal distribution and round your answers to two decimal places.
### Steps to Calculate the Confidence Interval:
#### A. Distribution Selection
To compute the confidence interval, use the [ Select ] distribution.
#### B. Confidence Interval Calculation
With 95% confidence, the mean number of hours that people who do not drink coffee get is between [ Select ] and [ Select ].
#### C. Confidence Interval Repetition
If many groups of 13 randomly selected people who do not drink coffee are surveyed, then a different confidence interval would be produced from each group. About [ Select ] percent of these confidence intervals will contain the true population mean number of hours of sleep per night and about [ Select ] percent will not contain the true population mean number of hours of sleep per night.
### Explanation
**Population Standard Deviation (σ):** 1.3 hours
**Sample Size (n):** 13
**Sample Mean (x̄)**: Calculate the average of the provided data set.
**95% Confidence Interval Formula:**
\[ CI = x̄ \pm Z \left( \frac{σ}{\sqrt{n}} \right) \]
Where:
- \( x̄ \) is the sample mean.
- \( Z \) is the Z-value corresponding to the 95% confidence level.
- \( σ \) is the population standard deviation.
- \( n \) is the sample size.
The interval provides a range in which we are 95% confident the true population mean falls.
### Completing the Steps
1. **Calculate the sample mean (x̄):**
Add the data points: 6 + 8 + 7 + 8 + 8 + 7 + 9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1a73d04-4829-40e4-8e78-0a30aa84e71e%2F87c740fd-1f1b-4068-a76b-614461c5362d%2Fkkfu9b_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating Confidence Interval for Sleep Hours of Non-Coffee Drinkers
The population standard deviation for the number of hours of sleep that people get per night is 1.3 hours. You are interested in finding a 95% confidence interval for the mean amount of sleep people who do not drink coffee get. The following data shows the results of a survey:
**Data Set:**
6, 8, 7, 8, 8, 7, 9, 5, 7, 8, 6, 7, 8
**Assumptions:**
- The standard deviation for people who do not drink coffee is the same as the standard deviation for the general population.
- Assume a normal distribution and round your answers to two decimal places.
### Steps to Calculate the Confidence Interval:
#### A. Distribution Selection
To compute the confidence interval, use the [ Select ] distribution.
#### B. Confidence Interval Calculation
With 95% confidence, the mean number of hours that people who do not drink coffee get is between [ Select ] and [ Select ].
#### C. Confidence Interval Repetition
If many groups of 13 randomly selected people who do not drink coffee are surveyed, then a different confidence interval would be produced from each group. About [ Select ] percent of these confidence intervals will contain the true population mean number of hours of sleep per night and about [ Select ] percent will not contain the true population mean number of hours of sleep per night.
### Explanation
**Population Standard Deviation (σ):** 1.3 hours
**Sample Size (n):** 13
**Sample Mean (x̄)**: Calculate the average of the provided data set.
**95% Confidence Interval Formula:**
\[ CI = x̄ \pm Z \left( \frac{σ}{\sqrt{n}} \right) \]
Where:
- \( x̄ \) is the sample mean.
- \( Z \) is the Z-value corresponding to the 95% confidence level.
- \( σ \) is the population standard deviation.
- \( n \) is the sample size.
The interval provides a range in which we are 95% confident the true population mean falls.
### Completing the Steps
1. **Calculate the sample mean (x̄):**
Add the data points: 6 + 8 + 7 + 8 + 8 + 7 + 9
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