Math Problem Statement

Less than 87% of workers indicate that they are mildly dissatisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).

Use the following codes to enter the following symbols: enter >= enter <= enter !=

Solution

To express the null and alternative hypotheses in symbolic form, we define pp as the proportion of workers who indicate that they are mildly dissatisfied with their job.

The hypotheses are as follows:

  • Null hypothesis H0H_0: The proportion of workers who are mildly dissatisfied is greater than or equal to 87%. H0:p87%H_0: p \geq 87\%

  • Alternative hypothesis H1H_1: The proportion of workers who are mildly dissatisfied is less than 87%. H1:p<87%H_1: p < 87\%

Would you like a detailed explanation of hypothesis testing or have any other questions?

Here are five related questions:

  1. What are the key steps in conducting a hypothesis test for population proportions?
  2. How do you calculate the test statistic for a proportion hypothesis test?
  3. What is the significance level (α\alpha) in hypothesis testing?
  4. How is the p-value interpreted in hypothesis testing?
  5. What is the difference between a one-tailed and two-tailed test?

Tip: Always clearly define the parameter of interest (like the proportion pp) before formulating hypotheses.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Population Proportion

Formulas

Null hypothesis H₀: p ≥ 87%
Alternative hypothesis H₁: p < 87%

Theorems

Proportion Hypothesis Testing Theorem

Suitable Grade Level

Undergraduate