Exercise 2.250 introduces a study showing thatfluoride exposure might have long-term negativeconsequences for the offspring of pregnant women.Part of the study examines the effect of adding flu-oride to tap water on mean fluoride concentrationin women. Summary statistics for fluoride concen-tration (measured in mg/L) for the two groups are given in Table 6.17. Find and interpret a 99% con-fidence interval for the mean increase in fluorideconcentration for those with fluoridated tap water. Answer the above questions in picture. Tap water Sample size mean St.Dev --------------- --------------- -------- ------ Fluoridated : 141 0.69 0.42 non-fluoridated 228 0.40 0.27 **Confidence Interval Upper Bound Calculation**To find the upper bound for this confidence interval, follow these steps:1. **Expression**: Calculate the value of \((\bar{x}_1 - \bar{x}_2) + ME\).2. **Definitions**: - \(\bar{x}_1\) represents the mean fluoride concentration in women who consume fluoridated water. - \(\bar{x}_2\) represents the mean fluoride concentration in women who consume non-fluoridated water.3. **Objective**: By computing the difference in means and adding the margin of error (ME), you determine the upper limit of the confidence interval for the difference in fluoride concentrations between the two groups. Use these definitions and expressions to correctly find the upper bound of the confidence interval. **Find the Lower Bound for this Confidence Interval**To determine the lower bound, calculate the following expression:\[(\bar{x}_1 - \bar{x}_2) - ME\]### Definitions- \(\bar{x}_1\): Mean fluoride concentration in women given fluoridated water.- \(\bar{x}_2\): Mean fluoride concentration in women given non-fluoridated water.Where \(ME\) represents the margin of error for the confidence interval calculation.

Answered: Exercise 2.250 introduces a study…

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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Question

Exercise 2.250 introduces a study showing that
fluoride exposure might have long-term negative
consequences for the offspring of pregnant women.
Part of the study examines the effect of adding flu-
oride to tap water on mean fluoride concentration
in women. Summary statistics for fluoride concen-
tration (measured in mg/L) for the two groups are given in Table 6.17. Find and interpret a 99% con-
fidence interval for the mean increase in fluoride
concentration for those with fluoridated tap water.
Answer the above questions in picture.
Tap water Sample size mean St.Dev
--------------- --------------- -------- ------

Fluoridated : 141 0.69 0.42

non-fluoridated 228 0.40 0.27

**Confidence Interval Upper Bound Calculation**

To find the upper bound for this confidence interval, follow these steps:

1. **Expression**: Calculate the value of \((\bar{x}_1 - \bar{x}_2) + ME\).

2. **Definitions**:
- \(\bar{x}_1\) represents the mean fluoride concentration in women who consume fluoridated water.
- \(\bar{x}_2\) represents the mean fluoride concentration in women who consume non-fluoridated water.

3. **Objective**: By computing the difference in means and adding the margin of error (ME), you determine the upper limit of the confidence interval for the difference in fluoride concentrations between the two groups.

Use these definitions and expressions to correctly find the upper bound of the confidence interval.

**Find the Lower Bound for this Confidence Interval**

To determine the lower bound, calculate the following expression:

\[
(\bar{x}_1 - \bar{x}_2) - ME
\]

### Definitions
- \(\bar{x}_1\): Mean fluoride concentration in women given fluoridated water.
- \(\bar{x}_2\): Mean fluoride concentration in women given non-fluoridated water.

Where \(ME\) represents the margin of error for the confidence interval calculation.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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