Assume that wve want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/2. (b) find the critical value za/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n= 190, x 29 7 hg, s = 6.6 hg. The confidence level is 95%.
Assume that wve want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/2. (b) find the critical value za/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n= 190, x 29 7 hg, s = 6.6 hg. The confidence level is 95%.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
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![### Constructing a Confidence Interval
#### Problem Statement
Assume that we want to construct a confidence interval. Do one of the following, as appropriate:
- (a) find the critical value \( t_{\alpha/2} \)
- (b) find the critical value \( z_{\alpha/2} \)
- (c) state that neither the normal distribution nor the t distribution applies.
#### Provided Data
Here are summary statistics for randomly selected weights of newborn girls:
- Sample size (\( n \)): 190
- Sample mean (\( \bar{x} \)): 29.7 hg
- Sample standard deviation (\( s \)): 6.6 hg
The confidence level is 95%.
#### Instructions
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
#### Options
- **A.** \( t_{\alpha/2} = \) [ ]
(Round to two decimal places as needed.)
- **B.** \( z_{\alpha/2} = \) [ ]
(Round to two decimal places as needed.)
- **C.** Neither the normal distribution nor the t distribution applies.
---
### Detailed Explanation of the Options
- **Option A: Using the t-distribution**
- The t-distribution is typically used when the sample size is small (\( n < 30 \)) and/or the population standard deviation is unknown.
- You need to find the critical value \( t_{\alpha/2} \) for the given confidence level and degrees of freedom (\( df = n - 1 \)).
- **Option B: Using the z-distribution**
- The z-distribution is used when the sample size is large (\( n \geq 30 \)) and the population standard deviation is known or can be approximated well by the sample standard deviation.
- You need to find the critical value \( z_{\alpha/2} \) for the given confidence level.
- **Option C: Neither distribution applies**
- This would be applicable in cases where the underlying assumptions for both the normal distribution (z-distribution) and t-distribution are violated or not met.
This kind of decision-making process is fundamental when performing inferential statistics to ensure that the resulting confidence intervals are valid based on the specified criteria and known data properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77118ecc-eadc-491f-9762-2009f6b89d99%2F3fbcd1ee-61a3-4c41-aa2c-7592faf79e71%2Fpmgeuzw.jpeg&w=3840&q=75)
Transcribed Image Text:### Constructing a Confidence Interval
#### Problem Statement
Assume that we want to construct a confidence interval. Do one of the following, as appropriate:
- (a) find the critical value \( t_{\alpha/2} \)
- (b) find the critical value \( z_{\alpha/2} \)
- (c) state that neither the normal distribution nor the t distribution applies.
#### Provided Data
Here are summary statistics for randomly selected weights of newborn girls:
- Sample size (\( n \)): 190
- Sample mean (\( \bar{x} \)): 29.7 hg
- Sample standard deviation (\( s \)): 6.6 hg
The confidence level is 95%.
#### Instructions
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
#### Options
- **A.** \( t_{\alpha/2} = \) [ ]
(Round to two decimal places as needed.)
- **B.** \( z_{\alpha/2} = \) [ ]
(Round to two decimal places as needed.)
- **C.** Neither the normal distribution nor the t distribution applies.
---
### Detailed Explanation of the Options
- **Option A: Using the t-distribution**
- The t-distribution is typically used when the sample size is small (\( n < 30 \)) and/or the population standard deviation is unknown.
- You need to find the critical value \( t_{\alpha/2} \) for the given confidence level and degrees of freedom (\( df = n - 1 \)).
- **Option B: Using the z-distribution**
- The z-distribution is used when the sample size is large (\( n \geq 30 \)) and the population standard deviation is known or can be approximated well by the sample standard deviation.
- You need to find the critical value \( z_{\alpha/2} \) for the given confidence level.
- **Option C: Neither distribution applies**
- This would be applicable in cases where the underlying assumptions for both the normal distribution (z-distribution) and t-distribution are violated or not met.
This kind of decision-making process is fundamental when performing inferential statistics to ensure that the resulting confidence intervals are valid based on the specified criteria and known data properties.
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