A random sample of 12 chemists from Washington stats shows an average salary of $39,420 with a population standard deviation of $1,659. A random sample of 26 chemists from New Mexico has an average salary of $30,215 with a population standard deviation of $4,116. Find the 98% confidence interval of the difference of means. **Statistical Input Form**This form is used for statistical calculations and consists of the following fields:1. **Mean Values:** - **Mean One (Washington):** - Type: Sample - Variable: $ x_1 $ - Input Box: [ ] - **Mean Two (New Mexico):** - Type: Sample - Variable: $ x_2 $ - Input Box: [ ]2. **Standard Deviations:** - **Standard Deviation One (Washington):** - Type: Population - Variable: $ \sigma_1 $ - Input Box: [ ] - **Standard Deviation Two (New Mexico):** - Type: Population - Variable: $ \sigma_2 $ - Input Box: [ ]3. **Sample Sizes:** - **Sample Size One (Cleveland):** - Variable: $ n_1 $ - Input Box: [ ] - **Sample Size Two (Philadelphia):** - Variable: $ n_2 $ - Input Box: [ ]4. **Rounding Calculations:** - **Round answer(s) to four decimal places:** - Formula: $ z \cdot (\alpha/2) $ - Function: invNorm - Input Boxes: [ ] , [ ] - Formula: $ z \cdot (\alpha/2) $ - Input Box: [ ] - **Round answer(s) to one decimal place (no commas):** - Difference in means: $ < \mu_1 - \mu_2 > $ - Input Box: [ ]This form is intended for performing statistical computations, allowing the user to input sample means, standard deviations, sample sizes, and desired rounding precision for results.

The sample mean one (Washington): x¯1=$39,420, sample mean two (New Mexico): x¯2=$30,215, population standard deviation one (Washington): σ1=$1,659, population standard deviation two (New Mexico): σ2=$4,116, sample size one (Washington): n1=12, sample size two (New Mexico): n2=26. Computation of critical value: 1-α=0.98α=0.02α2=0.011-α2=0.99 zα2=invNorm0.99,1,0 The critical value is 2.3263. zα2=2.3263.The 98% confidence interval of the difference of means is, x¯1-x¯2-zα2σ12n1+σ22n2<μ1-μ2<x¯1-x¯2+zα2σ12n1+σ22n239420-30215-2.32631659212+4116226<μ1-μ2<39420-30215+2.32631659212+41162269205-2183.4<μ1-μ2<9205+2183.47021.6<μ1-μ2<11388.4 Thus, the 98% confidence interval of the difference of means is 7021.6<μ1-μ2<11388.4.

Answered: A random sample of 12 chemists from…

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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A random sample of 12 chemists from Washington stats shows an average salary of $39,420 with a population standard deviation of $1,659. A random sample of 26 chemists from New Mexico has an average salary of $30,215 with a population standard deviation of $4,116. Find the 98% confidence interval of the difference of means.

**Statistical Input Form**

This form is used for statistical calculations and consists of the following fields:

1. **Mean Values:**
- **Mean One (Washington):**
- Type: Sample
- Variable: $ x_1 $
- Input Box: [ ]

- **Mean Two (New Mexico):**
- Type: Sample
- Variable: $ x_2 $
- Input Box: [ ]

2. **Standard Deviations:**
- **Standard Deviation One (Washington):**
- Type: Population
- Variable: $ \sigma_1 $
- Input Box: [ ]

- **Standard Deviation Two (New Mexico):**
- Type: Population
- Variable: $ \sigma_2 $
- Input Box: [ ]

3. **Sample Sizes:**
- **Sample Size One (Cleveland):**
- Variable: $ n_1 $
- Input Box: [ ]

- **Sample Size Two (Philadelphia):**
- Variable: $ n_2 $
- Input Box: [ ]

4. **Rounding Calculations:**
- **Round answer(s) to four decimal places:**
- Formula: $ z \cdot (\alpha/2) $
- Function: invNorm
- Input Boxes: [ ] , [ ]

- Formula: $ z \cdot (\alpha/2) $
- Input Box: [ ]

- **Round answer(s) to one decimal place (no commas):**
- Difference in means: $ < \mu_1 - \mu_2 > $
- Input Box: [ ]

This form is intended for performing statistical computations, allowing the user to input sample means, standard deviations, sample sizes, and desired rounding precision for results.

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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