Math Problem Statement

A software company is interested in improving customer satisfaction rate from the currently claimed. The company sponsored a survey of customers and found that customers were satisfied.What is the test statistic ?Round to two decimal places.

Solution

To determine the test statistic, we need to use the formula for a hypothesis test for a population proportion:

z=p^p0p0(1p0)nz = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}

Where:

  • p^=satisfied customerstotal customers surveyed\hat{p} = \frac{\text{satisfied customers}}{\text{total customers surveyed}} is the sample proportion.
  • p0p_0 is the claimed proportion (the population proportion under the null hypothesis).
  • nn is the number of customers surveyed.

Steps:

  1. Identify Variables:

    • The number of satisfied customers (xx).
    • The number of customers surveyed (nn).
    • The claimed proportion (p0p_0).
  2. Compute Sample Proportion (p^\hat{p}): p^=xn\hat{p} = \frac{x}{n}

  3. Compute Standard Error: SE=p0(1p0)nSE = \sqrt{\frac{p_0 (1 - p_0)}{n}}

  4. Calculate Test Statistic (zz): z=p^p0SEz = \frac{\hat{p} - p_0}{SE}

Please provide the specific values for the number of surveyed customers, satisfied customers, and the claimed satisfaction proportion, and I will calculate the test statistic for you.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Population Proportions
Z-Tests

Formulas

z = (\hat{p} - p_0) / \sqrt{(p_0(1 - p_0)) / n}
\hat{p} = x / n
SE = \sqrt{(p_0(1 - p_0)) / n}

Theorems

Z-Test for Proportions

Suitable Grade Level

Grades 11-12, College Level