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.