Use the Two-Proportions Z-Test to Perform the Required Hypothesis Test

question 54

Essay

Use the two-proportions z-test to perform the required hypothesis test. Assume that independent simple randomsamples have been selected from the two populations. Use the P-value approach.
- $\begin{array}{l} \text { Use the given sample data to test the claim that } \mathrm { p } _ { 1 } < \mathrm { p } _ { 2 } \text {. Use a significance level of } 0.10 \text {. }\\ \frac { \text { Sample 1 } } { \mathrm { n } _ { 1 } = 462 } \quad \frac { \text { Sample 2 } } { \mathrm { n } _ { 2 } = 380 }\\ x _ { 1 } = 84 \quad x _ { 2 } = 95 \end{array}$

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Definitions:

Inequality

An inequality is a mathematical statement indicating that two expressions are not equal, represented by symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).

Graphing Calculator

A handheld device capable of plotting graphs, solving equations, and performing other mathematical operations and visualizations.

Real Line

A linear continuum of points representing real numbers, effectively illustrating the concept of the infinite nature of real numbers on a one-dimensional scale.

Inequality

A mathematical expression that shows the relationship between two values that are not equal, using symbols such as <, >, ≤, or ≥.