### Constructing a Confidence Interval#### Problem StatementAssume 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 DataHere 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 hgThe confidence level is 95%.#### InstructionsSelect 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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Description: ### Constructing a Confidence Interval#### Problem StatementAssume 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

Given information- Sample size, n = 190 Sample mean, x-bar = 29.7 hg Sample standard deviation, s =…

Math

Statistics

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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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