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Here are summary statistics for randomly selected weights of newborn girls: n=36, x=3197.2 g, s=692.6 g. Use a confidence level of 99% to complete parts (a) through (d) a. Identify the critical value ta/2 used for finding the margin of error. ta/2=0 (Round to two decimal places as needed.)

Here are summary statistics for randomly selected weights of newborn girls: n=36, x=3197.2 g, s=692.6 g. Use a confidence level of 99% to complete parts (a) through (d) a. Identify the critical value ta/2 used for finding the margin of error. ta/2=0 (Round to two decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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**Summary Statistics for Newborn Weights** This content provides summary statistics for randomly selected weights of newborn girls. Let's break down the given information and address each part of the task. ### Statistical Data - **Sample size (n):** 36 - **Mean weight (\( \bar{x} \)):** 3197.2 g - **Standard deviation (s):** 692.6 g ### Task - **Confidence level:** 99% - **Goal:** Complete parts (a) through (d), focusing first on part (a). ### Part (a) **Identify the Critical Value (\( t_{\frac{\alpha}{2}} \))** In statistical analysis, the critical value is used to calculate the margin of error, which is essential for constructing confidence intervals. **Instructions:** - Calculate \( t_{\frac{\alpha}{2}} \) using the confidence level of 99%. - Round the critical value to two decimal places as needed. To complete this task, consult a t-distribution table or calculator with the given degrees of freedom (d.f. = \( n - 1 = 35 \)). **Note:** Typically, a t-distribution is used instead of a z-distribution when the sample size is small, or the population standard deviation is unknown. Here, the confidence interval will provide a range in which we expect the true mean weight to lie with 99% confidence. For educational inquiries or further assistance, please refer to provided examples or seek additional help as needed.
Transcribed Image Text:**Summary Statistics for Newborn Weights** This content provides summary statistics for randomly selected weights of newborn girls. Let's break down the given information and address each part of the task. ### Statistical Data - **Sample size (n):** 36 - **Mean weight (\( \bar{x} \)):** 3197.2 g - **Standard deviation (s):** 692.6 g ### Task - **Confidence level:** 99% - **Goal:** Complete parts (a) through (d), focusing first on part (a). ### Part (a) **Identify the Critical Value (\( t_{\frac{\alpha}{2}} \))** In statistical analysis, the critical value is used to calculate the margin of error, which is essential for constructing confidence intervals. **Instructions:** - Calculate \( t_{\frac{\alpha}{2}} \) using the confidence level of 99%. - Round the critical value to two decimal places as needed. To complete this task, consult a t-distribution table or calculator with the given degrees of freedom (d.f. = \( n - 1 = 35 \)). **Note:** Typically, a t-distribution is used instead of a z-distribution when the sample size is small, or the population standard deviation is unknown. Here, the confidence interval will provide a range in which we expect the true mean weight to lie with 99% confidence. For educational inquiries or further assistance, please refer to provided examples or seek additional help as needed.
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