---**Testing for Income Differences between Escambia and Miami-Dade Counties in Florida**An economist aims to determine if there is any difference in income between Escambia County and Miami-Dade County in Florida. For this purpose, random samples of residents from both counties are collected, and the following data is obtained. Both populations are assumed to be normally distributed with equal population variances.### Sample Data:**Escambia County (Population 1):**- Sample Size ($ n_1 $) = 11- Sample Mean ($ \bar{x}_1 $) = 36,700- Sample Standard Deviation ($ s_1 $) = 7800**Miami-Dade County (Population 2):**- Sample Size ($ n_2 $) = 15- Sample Mean ($ \bar{x}_2 $) = 34,700- Sample Standard Deviation ($ s_2 $) = 7375### Hypotheses Setup:To test the economist's claim, we set up the null and alternative hypotheses as follows:- **$ H_0 $: $ μ_1 - μ_2 = 0 $ versus $ H_a $: $ μ_1 - μ_2 ≠ 0 $**### Finding the Value of the Standardized Test Statistic:The standardized test statistic options provided are:- -2.713- 2.713- -0.64- 0.64- 0.67### Decision at a 5% Significance Level:To find the rejection region and state the decision:- **Reject $ H_0 $ if $ t < -2.064 $. Decision: Reject $ H_0 $.**- Reject $ H_0 $ if $ t < -1.711 $. Decision: Reject $ H_0 $.- Reject $ H_0 $ if $ -1.711 < t < 1.711 $. Decision: Do not reject $ H_0 $.- Reject $ H_0 $ if $ t ≥ 2.064 $. Decision: Do not reject $ H_0 $.- **Reject $ H_0 $ if $ t < -2.064 $ or $ t > 2.064 $. Decision: Do not reject $ H_0 $.**---Explanation:- The

An economist wants to test if there is any difference in income between Escambia county and Miami-Dade county in Florida. To do this, she collects random samples of residents from both these counties. The information collected from these samples is tabulated below. Assume that both the populations are normally distributed with equal population variances. Escambia County (Population 1) Miami-Dade County (Population 2) n₁ = 11 1₂ = 15 Z₁ = 36,700 $1 = 7800 7₂ = 34,700 82=7375 Set up the null and alternative hypotheses to test the economist's claim. Ho: ₁-₂-0 versus H₂:₁-₂0 ⒸH₂ : ₁ - ₂0 versus H₂ : ₁ - ₂ = 0 ⒸH₂ : ₁ - ₂ <0 versus H₂:₁-₂ 20 ⒸH₂: P-P₂20versus H₂ : ₁ - ₂ <0 ⒸH₂-H₂ ≤0 versus H₂ : ₁ - ₂ > 0 Find the value of the standardized test statistic. 0-2713 02713 0 064 0064 O 067 At 5% significance level, find the rejection region and state your decision Reject Hot-2.064. Decision: Reject Ho Reject Hit-1.711. Decision Reject H₂ Reject H₂ ft < -1.711 ort1.711. Decision: Do not reject H₂. O Reject Hot 2064. Decision: Do not reject Ho O Reject Hot-2.064 ort>2.064. Decision: Do not reject H₂.